The generator matrix

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

generates a code of length 45 over F4[X]/(X^2) who´s minimum homogenous weight is 121.

Homogenous weight enumerator: w(x)=1x^0+468x^121+456x^122+528x^123+861x^124+2040x^125+1500x^126+1848x^127+1728x^128+3540x^129+2940x^130+2448x^131+2283x^132+5052x^133+4236x^134+3492x^135+3066x^136+5448x^137+4500x^138+3588x^139+2409x^140+4572x^141+2760x^142+1620x^143+1305x^144+1728x^145+504x^146+300x^147+108x^148+192x^149+12x^152+3x^164

The gray image is a linear code over GF(4) with n=180, k=8 and d=121.
This code was found by Heurico 1.16 in 11.3 seconds.