The generator matrix

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

generates a code of length 45 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 117.

Homogenous weight enumerator: w(x)=1x^0+324x^117+204x^118+600x^119+1395x^120+2100x^121+1332x^122+2316x^123+4164x^124+6228x^125+3828x^126+6384x^127+7572x^128+12012x^129+8220x^130+11196x^131+13380x^132+19236x^133+12900x^134+17016x^135+17655x^136+23628x^137+13788x^138+15972x^139+13830x^140+16620x^141+7452x^142+6528x^143+6435x^144+5268x^145+1428x^146+1428x^147+987x^148+600x^149+57x^152+24x^156+18x^160+15x^164+3x^168

The gray image is a linear code over GF(4) with n=180, k=9 and d=117.
This code was found by Heurico 1.16 in 160 seconds.