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

generates a code of length 38 over F4[X,sigma]/(X^2) who�s minimum homogenous weight is 108.

Homogenous weight enumerator: w(x)=1x^0+141x^108+339x^112+504x^116+18x^124+9x^128+9x^140+3x^144

The gray image is a linear code over GF(4) with n=152, k=5 and d=108.
This code was found by Heurico 1.16 in 0.015 seconds.