The generator matrix

 1  0  1  1  1  1  1  1  1  0  1  1  1  0  1  1  X  1  1  1  1  1  1  1  0  1  1 a*X  X  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1
 0  1  1  a a^2  0 a^2*X+1 a^2*X+a^2  a  1  0 a^2*X+1  a  1 a^2*X+a^2 X+a  1 a^2*X+1  0 a^2*X+a^2 a^2*X+a^2  a  X a^2*X+1  1  X a*X+a  1  1 a*X+1 a*X+a X+1 a^2*X+a  1 X+a a^2*X+1 X+a a*X+1 a^2*X+a  1 X+a^2 a*X+a^2 a*X  a  0
 0  0 a^2*X  0  0  0  X  X  X  X  X  X a^2*X a^2*X a*X a^2*X a^2*X  0 a^2*X a*X a^2*X  0  X  0 a^2*X a*X  X  X a*X a*X  0 a^2*X  0  X a*X a^2*X  X  X a^2*X a^2*X a^2*X a^2*X  0 a^2*X a*X
 0  0  0  X  0  X a^2*X  0  X a^2*X  X  0 a*X a^2*X  0  0  X a*X  X  0 a^2*X  X a*X  0 a^2*X  X a*X  X a^2*X  X  X  0 a*X  0  X  X a^2*X  X a*X a^2*X a*X a^2*X a^2*X  0 a*X
 0  0  0  0 a^2*X a^2*X  X a^2*X a*X  0 a^2*X  X  X a*X  X  X  X  0  0 a*X  0 a*X a^2*X a*X a^2*X a^2*X  X a*X a*X a*X a^2*X a^2*X a*X a*X  0 a*X a*X a^2*X a*X a*X a^2*X  X  0 a^2*X  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+93x^120+432x^123+414x^124+1368x^127+669x^128+2136x^131+576x^132+3648x^135+972x^136+3312x^139+675x^140+1320x^143+465x^144+72x^147+123x^148+42x^152+27x^156+21x^160+9x^164+9x^168

The gray image is a linear code over GF(4) with n=180, k=7 and d=120.
This code was found by Heurico 1.16 in 0.938 seconds.