The generator matrix

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

generates a code of length 36 over F4[X]/(X^2) who´s minimum homogenous weight is 92.

Homogenous weight enumerator: w(x)=1x^0+39x^92+48x^95+381x^96+156x^98+480x^99+825x^100+336x^102+960x^103+1203x^104+936x^106+1824x^107+1893x^108+1104x^110+2064x^111+1872x^112+540x^114+768x^115+768x^116+69x^120+54x^124+36x^128+21x^132+6x^136

The gray image is a linear code over GF(4) with n=144, k=7 and d=92.
This code was found by Heurico 1.16 in 0.7 seconds.