The generator matrix

 1  0  0  0  1  1  1  1  1  1  1  1  1  X a*X  1  1  1  1  1  1  1  1  1  1  1  1  0 a*X  1  1  1 a^2*X  1  1  1
 0  1  0  0  X a^2*X a*X  X a^2*X a^2*X+1  a a*X+1 a*X+a^2  1  1  1 a^2*X+1 a^2*X a*X+1 X+1 a^2*X+a^2 a^2*X+1 a^2*X+a X+a^2 X+a a^2*X+a  a  1  X a^2 a*X a*X+1  1  X X+a^2 X+1
 0  0  1  0 a^2*X+1  X  0  a a*X a^2 X+a^2  1 a*X+a^2 X+1 a^2  X X+a a^2  X a*X a*X+1  a a^2*X+a  1 X+1 a^2*X+1 a^2*X+a a*X  1 a^2*X+1  1 a^2 a*X+a^2  X  0 a*X+1
 0  0  0  1 a^2 a^2*X+1  a X+a^2 a^2*X+a^2 a*X+a^2 a*X+a^2 a*X a^2*X+a a^2*X+1  1 a*X+a a^2 X+1  X a*X+1 a^2 X+1 a*X  0 a*X+a^2 a*X+1 a^2*X+1 X+a a^2*X+1  a a^2 X+a a*X+a a^2*X+a 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+2079x^96+7128x^100+12444x^104+18912x^108+17550x^112+6888x^116+516x^120+18x^128

The gray image is a linear code over GF(4) with n=144, k=8 and d=96.
This code was found by Heurico 1.16 in 434 seconds.