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 aX aX  1  1  1
 0  1  1  a (a+1)X+a+1  0 (a+1)X+1  a  X (a+1)X+a+1  1 (a+1)X+1 X+a aX+a+1  1  X (a+1)X (a+1)X aX+1 aX+1  1 X+a (a+1)X+a (a+1)X+a aX+a+1 a+1 a+1  1  1  1  0  X aX
 0  0 (a+1)X  X aX  X  0 (a+1)X aX (a+1)X (a+1)X  X aX  0 aX  X aX  0 (a+1)X  0  X (a+1)X aX  X (a+1)X aX  0 (a+1)X  0 aX aX  0  X

generates a code of length 33 over F4[X,sigma]/(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,sigma]/(X^2) for dimension 5.
This code was found by Heurico 1.16 in -1.01e-007 seconds.