The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 X 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1
0 2X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 0 2X 2X 2X 0 2X 2X 2X 0 2X 2X 2X 0 2X 2X 2X 0 0 0 2X 0 0 0 2X 0 0 0 2X 2X 0 0 2X 2X
0 0 2X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 0 0 0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 0 0 0 2X 0 0 0 2X 0 0 0 2X 0 0 0 0 0 0 2X 0 0 2X 0 0 2X 2X 2X 0 2X 0 0 0
0 0 0 2X 0 0 0 0 0 0 0 2X 2X 2X 2X 2X 2X 2X 2X 2X 0 2X 2X 0 0 2X 2X 2X 2X 0 0 0 0 0 0 0 0 0 0 0 0 0 2X 2X 2X 2X 2X 2X 2X 2X 0 2X 2X 0 0 2X 2X 0 0 2X 2X 0 0 2X 2X 0 0 0 0 0 2X 2X 2X 2X 2X 0 0 2X 2X 0 0 2X 0
0 0 0 0 2X 0 0 0 2X 2X 2X 2X 2X 0 2X 2X 0 0 0 0 0 0 0 0 0 2X 2X 2X 2X 0 0 0 2X 0 2X 0 0 0 2X 2X 2X 2X 2X 2X 0 0 2X 0 2X 0 2X 0 2X 2X 2X 0 2X 2X 2X 0 2X 2X 2X 0 2X 2X 0 0 2X 0 2X 2X 0 2X 0 2X 0 2X 0 0 0 0 0
0 0 0 0 0 2X 0 2X 2X 2X 0 0 0 0 2X 2X 2X 2X 0 0 0 2X 2X 2X 2X 2X 2X 0 0 2X 2X 0 2X 0 2X 0 2X 2X 2X 2X 0 0 0 0 2X 2X 2X 0 2X 0 0 0 2X 0 0 0 2X 0 2X 2X 0 2X 2X 2X 0 2X 0 2X 2X 2X 0 2X 0 0 2X 2X 0 2X 2X 2X 0 0 2X
0 0 0 0 0 0 2X 2X 0 2X 2X 0 2X 2X 2X 0 0 2X 0 2X 2X 2X 0 0 2X 0 2X 2X 0 0 2X 2X 0 0 2X 2X 2X 0 0 2X 2X 0 0 2X 0 2X 2X 2X 0 0 0 0 0 0 2X 2X 2X 2X 2X 2X 2X 2X 0 0 0 0 0 2X 0 2X 0 0 0 0 0 2X 0 0 2X 2X 2X 2X 0
generates a code of length 83 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 80.
Homogenous weight enumerator: w(x)=1x^0+78x^80+96x^82+768x^83+32x^86+48x^88+1x^160
The gray image is a code over GF(2) with n=664, k=10 and d=320.
This code was found by Heurico 1.16 in 75.9 seconds.