The generator matrix

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

generates a code of length 40 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 108.

Homogenous weight enumerator: w(x)=1x^0+2388x^108+7884x^112+12528x^116+16872x^120+17076x^124+7947x^128+840x^132

The gray image is a linear code over GF(4) with n=160, k=8 and d=108.
This code was found by Heurico 1.16 in 11.7 seconds.