The generator matrix

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

generates a code of length 45 over F4[X]/(X^2) who´s minimum homogenous weight is 124.

Homogenous weight enumerator: w(x)=1x^0+267x^124+420x^125+312x^126+1428x^128+1260x^129+732x^130+1596x^132+1488x^133+684x^134+1488x^136+1392x^137+660x^138+1485x^140+1020x^141+588x^142+729x^144+516x^145+96x^146+150x^148+48x^149+18x^152+6x^156

The gray image is a linear code over GF(4) with n=180, k=7 and d=124.
This code was found by Heurico 1.16 in 0.594 seconds.