The generator matrix

 1  0  0  1  1  1  1  1  1  1  1  1  1 a^2*X  1  1 a^2*X  1  1  1  0  1  1  1  1  0 a^2*X  1  1  0  1  1  1 a^2*X  1  1  1  1 a*X  X a*X  1  0  X  1
 0  1  0  0  0 a^2*X  1 a^2*X+a a^2 a^2*X+1 a^2*X+1  a a^2*X+a  1 a^2 a^2*X+a^2  1  1 a^2*X+a^2 a*X  1 a*X+1 a^2*X+a^2 X+a X+a  1  1  X X+a a^2*X X+a^2 a^2*X  a  1 a*X a^2*X+a a*X+a  0  1  1  1 a^2*X+a  1  1 a^2*X+a
 0  0  1  1  a a^2  1 X+1  1  a  0  X a^2 a^2 a*X+a^2 a*X+a X+1 a^2  0 X+a^2  a  X X+1 a^2  1 X+1  X X+a a^2*X  1 a*X+a^2  1 X+a a^2*X+a^2 a^2*X+1  a a^2*X+1 a*X+a a^2*X+1 a*X+a X+1 a*X+1 a*X+1 X+a a^2
 0  0  0 a^2*X  0  0  0  X  X  X a^2*X a*X a^2*X a^2*X a*X a*X a*X  X a^2*X  X  X  0 a^2*X a^2*X  0 a*X a^2*X  X  0 a^2*X a^2*X  X  0  0 a*X a^2*X a^2*X a*X a^2*X  X a^2*X a*X  X  0  X
 0  0  0  0  X a^2*X a*X  X a^2*X a*X a*X  X  X a*X a*X  0  X a^2*X  X  X  0 a^2*X a^2*X  0  0 a*X  0  X a^2*X  X a*X a*X a*X  X  0  0  X a*X a*X a*X  0  0  0 a^2*X a*X

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

Homogenous weight enumerator: w(x)=1x^0+294x^120+564x^121+276x^122+384x^123+1296x^124+2244x^125+720x^126+912x^127+2526x^128+4128x^129+1560x^130+1776x^131+3912x^132+6000x^133+2400x^134+2544x^135+4755x^136+7380x^137+2628x^138+2544x^139+4719x^140+5412x^141+1392x^142+960x^143+1608x^144+1752x^145+240x^146+96x^147+243x^148+168x^149+39x^152+36x^156+3x^160+15x^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 12.2 seconds.