The generator matrix

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

generates a code of length 37 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 108.

Homogenous weight enumerator: w(x)=1x^0+576x^108+216x^112+132x^116+84x^120+12x^124+3x^128

The gray image is a linear code over GF(4) with n=148, k=5 and d=108.
This code was found by Heurico 1.16 in 6.48 seconds.