The generator matrix

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

generates a code of length 36 over F4[X]/(X^2) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+123x^88+291x^92+468x^96+192x^97+402x^100+1152x^101+498x^104+3072x^105+531x^108+4992x^109+450x^112+2880x^113+531x^116+399x^120+234x^124+141x^128+27x^132

The gray image is a linear code over GF(4) with n=144, k=7 and d=88.
This code was found by Heurico 1.16 in 1.38 seconds.