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

generates a code of length 35 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 92.

Homogenous weight enumerator: w(x)=1x^0+105x^92+171x^96+192x^99+195x^100+1152x^103+153x^104+1728x^107+108x^108+84x^112+75x^116+69x^120+33x^124+18x^128+12x^132

The gray image is a linear code over GF(4) with n=140, k=6 and d=92.
This code was found by Heurico 1.16 in 0.0937 seconds.