The generator matrix

 1  0  0  0  1  1  1  X  1 aX  1  1  1  1  1  1  1  1  1  1  1  1  1  1 aX  1  0  1  1  1  1  1  1  1  1  X  1  1  1
 0  1  0  0  X  1 X+1  1 (a+1)X  1 (a+1)X+1 (a+1)X+a a+1 aX  1 X+a a+1 aX+a  X X+1  0 X+1 X+a (a+1)X+a+1  1  a aX (a+1)X+a+1 X+a+1 (a+1)X+a  1 (a+1)X (a+1)X+a  X X+a  1 a+1 X+a aX
 0  0  1  0 (a+1)X+1  1 (a+1)X (a+1)X+1 aX+1  a aX aX+a a+1  0 X+a X+1 X+1 (a+1)X aX+a+1 X+a+1 (a+1)X+a+1 (a+1)X+a+1  0 (a+1)X+a a+1 X+a  1 aX+1 aX+a X+a+1 a+1  1 (a+1)X  a a+1 (a+1)X+a  1 X+1  1
 0  0  0  1 a+1  X aX+a+1 aX+a+1  a aX (a+1)X+a aX+1  1 X+1 aX+a aX+1 X+1 X+a+1 X+a X+a X+a+1 (a+1)X (a+1)X  X (a+1)X+a+1 (a+1)X a+1 (a+1)X+a a+1  1 X+a+1 aX+a aX+a aX+a+1 aX  a X+a+1 aX+a (a+1)X+1

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

Homogenous weight enumerator: w(x)=1x^0+507x^104+1044x^105+672x^106+960x^107+1869x^108+2808x^109+900x^110+1668x^111+3042x^112+4728x^113+1896x^114+3192x^115+4998x^116+6312x^117+2904x^118+3648x^119+5454x^120+6300x^121+2304x^122+2376x^123+3048x^124+2976x^125+516x^126+444x^127+513x^128+408x^129+24x^130+18x^132+3x^136+3x^140

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 10.1 seconds.