The generator matrix

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

generates a code of length 39 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 107.

Homogenous weight enumerator: w(x)=1x^0+552x^107+528x^108+96x^109+480x^110+1524x^111+1035x^112+204x^113+624x^114+2136x^115+1212x^116+156x^117+432x^118+2112x^119+1137x^120+228x^121+528x^122+1632x^123+696x^124+84x^125+240x^126+492x^127+228x^128+12x^132+15x^136

The gray image is a linear code over GF(4) with n=156, k=7 and d=107.
This code was found by Heurico 1.16 in 26.9 seconds.