The generator matrix

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

generates a code of length 45 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 120.

Homogenous weight enumerator: w(x)=1x^0+66x^120+24x^122+216x^123+474x^124+240x^126+828x^127+1104x^128+480x^130+1032x^131+1236x^132+912x^134+1608x^135+2037x^136+1032x^138+1656x^139+1575x^140+384x^142+732x^143+465x^144+72x^147+78x^148+72x^152+33x^156+12x^160+12x^164+3x^168

The gray image is a linear code over GF(4) with n=180, k=7 and d=120.
This code was found by Heurico 1.16 in 0.943 seconds.