The generator matrix

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

generates a code of length 37 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 104.

Homogenous weight enumerator: w(x)=1x^0+54x^104+48x^105+78x^108+288x^109+84x^112+432x^113+12x^120+12x^124+3x^128+6x^136+6x^140

The gray image is a linear code over GF(4) with n=148, k=5 and d=104.
This code was found by Heurico 1.16 in 0.016 seconds.