The generator matrix

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

generates a code of length 33 over F4[X]/(X^2) who´s minimum homogenous weight is 96.

Homogenous weight enumerator: w(x)=1x^0+123x^96+576x^97+81x^100+36x^104+192x^105+12x^108+3x^132

The gray image is a linear code over GF(4) with n=132, k=5 and d=96.
As d=96 is an upper bound for linear (132,5,4)-codes, this code is optimal over F4[X]/(X^2) for dimension 5.
This code was found by Heurico 1.16 in -3.62e-008 seconds.