The generator matrix

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

generates a code of length 45 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 112.

Homogenous weight enumerator: w(x)=1x^0+69x^112+225x^116+12x^118+354x^120+132x^122+411x^124+792x^126+474x^128+1992x^130+393x^132+3900x^134+438x^136+3828x^138+450x^140+1632x^142+462x^144+393x^148+231x^152+135x^156+42x^160+9x^164+9x^168

The gray image is a linear code over GF(4) with n=180, k=7 and d=112.
This code was found by Heurico 1.16 in 1.83 seconds.