The generator matrix

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

generates a code of length 34 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 97.

Homogenous weight enumerator: w(x)=1x^0+84x^97+216x^98+27x^100+180x^101+192x^102+24x^104+60x^105+120x^106+9x^108+60x^109+48x^110+3x^120

The gray image is a linear code over GF(4) with n=136, k=5 and d=97.
This code was found by Heurico 1.16 in 0.033 seconds.