The generator matrix

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

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+267x^104+216x^106+990x^108+672x^110+1602x^112+1440x^114+2757x^116+2160x^118+2859x^120+1416x^122+1440x^124+240x^126+186x^128+60x^132+42x^136+30x^140+3x^144+3x^148

The gray image is a linear code over GF(4) with n=156, k=7 and d=104.
This code was found by Heurico 1.16 in 0.8 seconds.