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  0 (a+1)X  X  X  1 (a+1)X
 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  1  X  1  1 X+a  1
 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  1  1 (a+1)X a+1  1  a
 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  1  1 aX+1 (a+1)X+1 X+a (a+1)X+a+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+645x^104+792x^105+888x^106+408x^107+2073x^108+2448x^109+2196x^110+648x^111+4143x^112+3564x^113+3672x^114+1116x^115+5955x^116+5388x^117+4920x^118+1260x^119+6840x^120+5100x^121+3960x^122+1020x^123+3822x^124+2292x^125+1236x^126+156x^127+570x^128+384x^129+24x^130+3x^132+9x^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 12.7 seconds.