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

generates a code of length 46 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 120.

Homogenous weight enumerator: w(x)=1x^0+303x^120+324x^121+708x^122+1092x^123+1800x^124+2340x^125+3180x^126+3084x^127+4809x^128+5160x^129+6984x^130+7464x^131+10485x^132+9624x^133+12516x^134+12792x^135+16344x^136+15768x^137+17496x^138+17460x^139+19140x^140+15876x^141+16452x^142+13884x^143+13671x^144+9528x^145+8376x^146+4896x^147+4599x^148+2592x^149+1836x^150+768x^151+426x^152+228x^153+36x^154+45x^156+27x^160+24x^164+3x^168+3x^172

The gray image is a linear code over GF(4) with n=184, k=9 and d=120.
This code was found by Heurico 1.16 in 163 seconds.