The generator matrix

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

generates a code of length 35 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 96.

Homogenous weight enumerator: w(x)=1x^0+156x^96+168x^97+96x^98+456x^100+444x^101+192x^102+411x^104+348x^105+288x^106+423x^108+372x^109+192x^110+270x^112+204x^113+45x^116+15x^120+9x^124+3x^128+3x^132

The gray image is a linear code over GF(4) with n=140, k=6 and d=96.
This code was found by Heurico 1.16 in 0.0483 seconds.