The generator matrix

 1  0  0  1  1  1  1  1  1  1  0  1  1  1  1  1  1 (a+1)X (a+1)X  1  1  1  1  1  0  1  1  1  1  1  X  1  1  1
 0  1  0  1  a a+1 (a+1)X (a+1)X a+1 (a+1)X+a  1  a  0 (a+1)X+1 (a+1)X+a+1 (a+1)X+a (a+1)X+a+1  1  1 (a+1)X+1 aX a+1 (a+1)X+a  X (a+1)X X+a (a+1)X+a+1 aX+a (a+1)X+a+1 aX  1 X+1  a (a+1)X
 0  0  1 a+1  a  1 a+1  1 X+a+1  1  a  0 X+a  X  X a+1  a  1 a+1 aX+a+1 X+a X+a (a+1)X X+1  1 aX+a+1 X+a+1  1 aX+a+1 aX (a+1)X+1 (a+1)X (a+1)X+a+1 a+1
 0  0  0  X  0  X  0  0 (a+1)X aX aX (a+1)X (a+1)X  X  X (a+1)X  0 aX (a+1)X  X aX (a+1)X  X aX  X aX  X  X aX  0  0  0 aX (a+1)X
 0  0  0  0  X (a+1)X aX (a+1)X (a+1)X  X  X  0 (a+1)X  X aX  X  0  0 aX aX  X aX  0 aX  0 aX  X  0  0  X  X  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 88.

Homogenous weight enumerator: w(x)=1x^0+231x^88+480x^89+228x^90+528x^91+1149x^92+1920x^93+1032x^94+1164x^95+2907x^96+4728x^97+1608x^98+1920x^99+4743x^100+7824x^101+2832x^102+2712x^103+6162x^104+8736x^105+2676x^106+2256x^107+3543x^108+3696x^109+840x^110+636x^111+588x^112+264x^113+57x^116+51x^120+12x^124+12x^128

The gray image is a linear code over GF(4) with n=136, k=8 and d=88.
This code was found by Heurico 1.16 in 9.01 seconds.