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

generates a code of length 40 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 100.

Homogenous weight enumerator: w(x)=1x^0+114x^100+330x^104+12x^105+453x^108+180x^109+435x^112+1080x^113+486x^116+3240x^117+462x^120+4860x^121+516x^124+2916x^125+483x^128+372x^132+240x^136+159x^140+33x^144+12x^148

The gray image is a linear code over GF(4) with n=160, k=7 and d=100.
This code was found by Heurico 1.16 in 1.61 seconds.