The generator matrix

 1  0  0  1  1  1  1  1  1  1 a^2*X  1  1  1  1  1  1 a^2*X  1  1  1 a^2*X  1  1  1  1  1  1  0  1 a*X  0  1  1
 0  1  0  1  a a^2 a^2*X a^2*X  1 a^2*X+a  1  a  0 a^2*X+a^2 a^2*X+1 a^2*X+a a^2*X+1  1 a*X+a a^2  1  1  a X+a a^2*X+a^2 a^2*X+1  1 a^2*X+1  1 a^2*X+a^2  1  1  X  1
 0  0  1 a^2  a  1  1 a^2 X+1 a^2 a^2  0 X+a  0  X  1  a  1 a^2*X a*X+a^2 a*X+a a^2*X+1 X+a X+a a^2*X  0 a^2  X  1 a^2*X+a  a a^2*X X+a a^2*X+a^2
 0  0  0  X  0  X  0  0 a^2*X a*X a^2*X a^2*X a^2*X  X  X a^2*X  0 a^2*X a*X  0 a^2*X a*X  X  0 a*X  0 a*X  X  X  0  X a^2*X  X a*X
 0  0  0  0  X a^2*X a*X a^2*X  X  0  0 a*X  X a*X  X a^2*X  0 a*X a^2*X  X  0 a^2*X  X a*X  0  X a^2*X a^2*X a*X a^2*X  X  0  0  0

generates a code of length 34 over F4[X]/(X^2) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+372x^88+240x^89+336x^90+696x^91+1503x^92+876x^93+1176x^94+1680x^95+4059x^96+1848x^97+2496x^98+2256x^99+7335x^100+3960x^101+3600x^102+3840x^103+9381x^104+3456x^105+3504x^106+3000x^107+5148x^108+1788x^109+1176x^110+816x^111+750x^112+120x^113+57x^116+33x^120+15x^124+12x^128+6x^132

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 8.56 seconds.