The generator matrix

 1  0  1  1  1  1  1  1  1  0  1  1  1  0  1  1  0  1  1  1  X  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  1  1  a a+1  0 (a+1)X+1 (a+1)X+a+1  a  1  0 (a+1)X+1 (a+1)X+a+1  1  a  0  1 (a+1)X+a+1 (a+1)X+1  a  1 (a+1)X+a+1  X  X aX+a+1 X+a+1 a+1 X+a (a+1)X+1 a+1 (a+1)X+a X+1 aX+1  0
 0  0 (a+1)X  0  0  0  X aX  X  X  X (a+1)X (a+1)X (a+1)X  0  0 aX (a+1)X (a+1)X (a+1)X  0 (a+1)X  X aX  X (a+1)X  X  X  X aX  0  0  0  0
 0  0  0  X  0  X (a+1)X (a+1)X  X (a+1)X  0 (a+1)X  X  0 aX  X  X aX (a+1)X (a+1)X (a+1)X  0  X  X aX  0 (a+1)X (a+1)X  0 aX aX (a+1)X  X aX
 0  0  0  0 (a+1)X (a+1)X (a+1)X (a+1)X  0 aX  X aX  0 aX  0 aX aX  X  0  X  X (a+1)X (a+1)X aX  0  X  0 aX (a+1)X  X aX aX  0 (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+78x^88+96x^89+204x^91+324x^92+408x^93+744x^95+498x^96+912x^97+1320x^99+1098x^100+1920x^101+2208x^103+1218x^104+2064x^105+1452x^107+630x^108+744x^109+216x^111+126x^112+54x^116+48x^120+6x^124+15x^128

The gray image is a linear code over GF(4) with n=136, k=7 and d=88.
This code was found by Heurico 1.16 in 0.68 seconds.