The generator matrix

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

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+996x^108+1404x^112+660x^116+708x^120+312x^124+15x^128

The gray image is a linear code over GF(4) with n=152, k=6 and d=108.
This code was found by Heurico 1.16 in 1.17 seconds.