The generator matrix

 1  0  0  0  1  1  1  X  1 a^2*X  1  1  1  1  1  X  1  1  1  1  1  1  0  1  X  1  1  1  0  1  1  1  1 a^2*X  1  1  1  1  0
 0  1  0  0  X  1 X+1  1 a*X  1 a^2*X+a X+a^2 a^2 a*X+1 a^2*X+1  1 X+a a^2*X  1 a^2 a^2*X+a^2 X+a^2  1 X+1 a*X X+a^2 a*X+a a^2*X  1  a  1 a*X+a a^2  1 X+a a^2*X a*X+1  a a*X
 0  0  1  0 a^2*X+1  1 a^2*X a^2*X+1 X+1 a^2*X+a a^2*X+a^2  X a^2*X+a^2 X+a a^2 a^2*X+a  0 a^2*X X+a^2 X+a^2 a*X+a a^2*X+a a*X  a  1 a^2*X+1 a^2*X+a a^2*X+1 a^2 a*X+a a*X+1 a*X+a^2 a^2*X+a  1 a*X a^2*X+a^2 a^2 a^2*X a^2*X
 0  0  0  1 a^2  X a*X+a^2 a*X+a^2  a a^2*X X+a a^2*X+a^2 a^2*X+1 a*X+1 a*X+a^2 a^2*X+a X+1 a*X+1 a*X a*X+a^2  1 a^2*X a*X+1 a^2*X X+1  X  1 a^2*X  a a^2*X+a^2 X+a^2 X+1 a^2*X+a a*X+1 a^2*X+a a^2  a  0  1

generates a code of length 39 over F4[X]/(X^2) who´s minimum homogenous weight is 104.

Homogenous weight enumerator: w(x)=1x^0+627x^104+564x^105+1008x^106+720x^107+2325x^108+1752x^109+1800x^110+1200x^111+4437x^112+3144x^113+3444x^114+2340x^115+6369x^116+3948x^117+4260x^118+2964x^119+7071x^120+3792x^121+3612x^122+1692x^123+4011x^124+1932x^125+1092x^126+300x^127+738x^128+228x^129+144x^130+15x^132+6x^136

The gray image is a linear code over GF(4) with n=156, k=8 and d=104.
This code was found by Heurico 1.16 in 9.88 seconds.