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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  X  X  X  X  X  X  X  X  1  2  1  X  2  1  X  1  1  1  1  1  1  2  X  X  X  1  1  1
 0  2  0  0  0  0  0  0  0  0  0  0  0  0  2  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  0  2  2  2  2  0  2  0  0  0  2  2  2  0  2  2  2  0  0  2  0  2  2  2  0  0  0  2  0  2  0  0  0  0  2  2  2  0  2  0  0  2  2  0  0  0  0  0
 0  0  2  0  0  0  0  0  0  0  0  0  0  0  2  0  0  0  0  2  2  2  2  2  2  2  0  0  0  2  0  0  0  2  2  2  0  0  0  2  2  2  0  2  2  0  0  2  2  2  2  0  0  0  2  0  2  0  0  2  2  2  0  0  2  0  0  0  2  2  0  0  0  0  2  2  0  0  0
 0  0  0  2  0  0  0  0  0  0  0  0  0  2  0  0  0  2  2  2  2  2  2  0  0  0  0  2  0  2  2  2  0  2  0  0  2  2  0  0  0  2  2  2  0  2  0  2  2  0  2  2  2  0  0  0  0  0  0  0  2  0  2  0  2  0  2  2  0  2  2  2  0  2  0  2  0  0  0
 0  0  0  0  2  0  0  0  0  0  0  0  0  2  0  2  2  2  2  2  2  0  2  2  0  2  2  2  0  0  0  2  2  2  2  2  0  2  2  0  0  0  2  0  0  0  0  2  0  0  0  0  0  2  0  2  2  2  2  0  2  0  0  2  0  2  2  2  0  0  0  0  2  0  2  2  2  0  0
 0  0  0  0  0  2  0  0  0  0  0  0  2  0  0  2  2  0  2  2  0  2  0  2  0  2  2  2  2  0  0  2  2  0  0  0  2  0  2  0  0  0  0  2  2  0  2  2  2  2  2  0  0  0  0  0  2  2  0  0  2  2  2  0  0  0  2  0  2  2  0  0  0  2  0  2  2  0  0
 0  0  0  0  0  0  2  0  0  0  0  0  2  0  0  0  2  2  2  2  0  2  2  0  2  0  2  0  0  2  0  0  2  2  2  0  0  0  0  2  0  0  0  2  2  2  2  0  2  0  0  0  2  0  0  2  0  2  2  2  2  2  2  0  2  2  2  0  0  2  2  2  2  2  2  2  0  2  2
 0  0  0  0  0  0  0  2  0  0  0  2  0  0  0  0  2  2  0  2  0  0  0  2  2  2  0  0  2  0  2  2  2  2  0  0  0  2  2  2  2  2  0  0  0  0  2  2  2  2  2  0  2  2  2  0  0  2  2  2  2  2  0  0  2  0  2  0  0  0  2  2  2  0  0  2  2  2  2
 0  0  0  0  0  0  0  0  2  0  0  2  0  0  0  2  0  0  2  0  2  0  0  2  0  0  0  0  2  2  2  0  0  2  2  0  2  2  2  2  0  0  0  2  2  2  2  0  2  0  2  2  2  2  2  0  0  0  0  2  2  0  0  2  2  2  0  0  2  0  2  2  0  2  2  2  0  0  0
 0  0  0  0  0  0  0  0  0  2  0  2  2  2  2  2  0  0  0  2  0  0  2  2  0  0  2  0  2  2  0  0  2  2  0  2  2  0  0  0  0  2  0  0  0  2  0  2  0  2  2  2  0  0  2  2  0  2  0  2  2  0  0  0  0  2  0  2  0  0  2  2  0  2  2  0  2  0  0
 0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  0  0  2  2  2  2  2  0  2  0  2  0  0  0  0  0  2  0  2  0  0  2  0  2  2  0  0  0  2  0  0  2  0  0  2  0  0  2  2  0  2  2  2  2  2  0  2  0  2  2  2  2  2  2  0  2  0  0  2  2  2  0  0  0

generates a code of length 79 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+110x^64+2x^66+255x^68+38x^70+457x^72+222x^74+1067x^76+1878x^78+2223x^80+814x^82+479x^84+98x^86+274x^88+18x^90+157x^92+2x^94+66x^96+26x^100+4x^104+1x^120

The gray image is a code over GF(2) with n=316, k=13 and d=128.
This code was found by Heurico 1.16 in 9.48 seconds.