The generator matrix

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

generates a code of length 34 over F4[X]/(X^2) who´s minimum homogenous weight is 89.

Homogenous weight enumerator: w(x)=1x^0+384x^89+348x^90+720x^91+1104x^92+1740x^93+1332x^94+2196x^95+2130x^96+3552x^97+2520x^98+3792x^99+3582x^100+5112x^101+4584x^102+5112x^103+4752x^104+5664x^105+3852x^106+4032x^107+2835x^108+3036x^109+1188x^110+1044x^111+423x^112+480x^113+12x^116+6x^120+3x^124

The gray image is a linear code over GF(4) with n=136, k=8 and d=89.
This code was found by Heurico 1.16 in 8.43 seconds.