The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+480x^86+552x^87+816x^88+936x^89+3048x^90+2496x^91+2436x^92+3480x^93+9048x^94+7284x^95+6042x^96+9132x^97+18456x^98+15456x^99+9783x^100+16944x^101+30816x^102+22992x^103+12195x^104+17184x^105+26088x^106+14784x^107+7620x^108+7320x^109+9576x^110+4020x^111+1941x^112+300x^113+792x^114+69x^116+36x^120+6x^124+6x^128+6x^132+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 114 seconds.