The generator matrix

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

generates a code of length 46 over F4[X]/(X^2) who´s minimum homogenous weight is 124.

Homogenous weight enumerator: w(x)=1x^0+171x^124+72x^126+372x^127+660x^128+324x^130+780x^131+1089x^132+624x^134+1128x^135+1536x^136+840x^138+2040x^139+1806x^140+936x^142+1380x^143+1359x^144+276x^146+444x^147+384x^148+66x^152+42x^156+24x^160+9x^164+12x^168+3x^172+6x^176

The gray image is a linear code over GF(4) with n=184, k=7 and d=124.
This code was found by Heurico 1.16 in 0.967 seconds.