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

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+2484x^108+7782x^112+11988x^116+18000x^120+16476x^124+7875x^128+924x^132+6x^144

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 55.1 seconds.