The generator matrix

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

generates a code of length 34 over F4[X]/(X^2) who´s minimum homogenous weight is 97.

Homogenous weight enumerator: w(x)=1x^0+84x^97+216x^98+27x^100+180x^101+192x^102+24x^104+60x^105+120x^106+9x^108+60x^109+48x^110+3x^120

The gray image is a linear code over GF(4) with n=136, k=5 and d=97.
This code was found by Heurico 1.16 in 0.047 seconds.