The generator matrix

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

generates a code of length 45 over F4[X]/(X^2) who´s minimum homogenous weight is 128.

Homogenous weight enumerator: w(x)=1x^0+585x^128+336x^130+972x^132+468x^134+507x^136+156x^138+408x^140+108x^142+384x^144+84x^146+84x^148+3x^152

The gray image is a linear code over GF(4) with n=180, k=6 and d=128.
This code was found by Heurico 1.16 in 0.109 seconds.