The generator matrix

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

generates a code of length 34 over F4[X]/(X^2) who´s minimum homogenous weight is 93.

Homogenous weight enumerator: w(x)=1x^0+96x^93+252x^94+96x^96+360x^97+504x^98+57x^100+360x^101+720x^102+45x^104+504x^105+648x^106+30x^108+216x^109+180x^110+3x^112+15x^120+6x^124+3x^132

The gray image is a linear code over GF(4) with n=136, k=6 and d=93.
This code was found by Heurico 1.16 in 4.17 seconds.