The generator matrix

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

generates a code of length 34 over F4[X]/(X^2) who´s minimum homogenous weight is 92.

Homogenous weight enumerator: w(x)=1x^0+315x^92+552x^93+588x^94+1113x^96+1272x^97+936x^98+1239x^100+1668x^101+1440x^102+1587x^104+1524x^105+1176x^106+1164x^108+996x^109+468x^110+192x^112+132x^113+15x^116+3x^120+3x^124

The gray image is a linear code over GF(4) with n=136, k=7 and d=92.
This code was found by Heurico 1.16 in 0.422 seconds.