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

generates a code of length 38 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 104.

Homogenous weight enumerator: w(x)=1x^0+393x^104+492x^105+660x^106+336x^107+1080x^108+996x^109+972x^110+360x^111+1314x^112+1092x^113+1188x^114+360x^115+1365x^116+1092x^117+1284x^118+312x^119+1125x^120+768x^121+504x^122+168x^123+330x^124+168x^125+15x^128+9x^132

The gray image is a linear code over GF(4) with n=152, k=7 and d=104.
This code was found by Heurico 1.16 in 1.11 seconds.