The generator matrix

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

generates a code of length 34 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+408x^86+588x^87+474x^88+1092x^89+2724x^90+3348x^91+1689x^92+4584x^93+8112x^94+8844x^95+4698x^96+10776x^97+15156x^98+18264x^99+9219x^100+20832x^101+22920x^102+24948x^103+11544x^104+21060x^105+20796x^106+19380x^107+6399x^108+8664x^109+8880x^110+4500x^111+687x^112+576x^113+876x^114+45x^116+27x^120+24x^124+6x^128+3x^136

The gray image is a linear code over GF(4) with n=136, k=9 and d=86.
This code was found by Heurico 1.16 in 160 seconds.