The generator matrix

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

generates a code of length 34 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 96.

Homogenous weight enumerator: w(x)=1x^0+768x^96+468x^98+948x^100+348x^102+354x^104+204x^106+708x^108+132x^110+165x^112

The gray image is a linear code over GF(4) with n=136, k=6 and d=96.
This code was found by Heurico 1.16 in 4.66 seconds.