The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+240x^117+564x^118+228x^119+603x^120+2100x^121+2796x^122+1536x^123+2799x^124+6228x^125+8652x^126+3900x^127+5922x^128+11964x^129+14796x^130+6564x^131+9777x^132+19092x^133+22680x^134+10236x^135+12570x^136+23964x^137+24036x^138+9384x^139+10959x^140+17004x^141+14412x^142+4548x^143+3939x^144+4980x^145+3972x^146+468x^147+417x^148+444x^149+252x^150+42x^152+42x^156+18x^160+6x^164+9x^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 152 seconds.