The generator matrix

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

generates a code of length 45 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 132.

Homogenous weight enumerator: w(x)=1x^0+522x^132+324x^136+54x^140+123x^144

The gray image is a linear code over GF(4) with n=180, k=5 and d=132.
This code was found by Heurico 1.16 in 3.11 seconds.