The generator matrix

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

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+54x^120+159x^124+48x^126+207x^128+432x^130+138x^132+1296x^134+126x^136+1296x^138+72x^140+102x^144+66x^148+24x^152+33x^156+18x^160+12x^164+12x^168

The gray image is a linear code over GF(4) with n=180, k=6 and d=120.
This code was found by Heurico 1.16 in 0.13 seconds.