The generator matrix

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

generates a code of length 36 over F4[X]/(X^2) who´s minimum homogenous weight is 96.

Homogenous weight enumerator: w(x)=1x^0+162x^96+174x^100+174x^104+768x^105+147x^108+2304x^109+102x^112+72x^116+66x^120+66x^124+39x^128+18x^132+3x^140

The gray image is a linear code over GF(4) with n=144, k=6 and d=96.
This code was found by Heurico 1.16 in 0.302 seconds.