The generator matrix

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

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+465x^120+156x^121+144x^122+468x^123+2391x^124+1020x^125+792x^126+1212x^127+4686x^128+1764x^129+780x^130+2364x^131+6540x^132+2616x^133+1584x^134+3528x^135+9282x^136+3588x^137+1608x^138+3324x^139+7491x^140+2604x^141+984x^142+1308x^143+3324x^144+540x^145+252x^146+84x^147+534x^148+39x^152+27x^156+21x^160+6x^164+6x^168+3x^172

The gray image is a linear code over GF(4) with n=180, k=8 and d=120.
This code was found by Heurico 1.16 in 12.9 seconds.