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

generates a code of length 44 over F4[X]/(X^2) who´s minimum homogenous weight is 124.

Homogenous weight enumerator: w(x)=1x^0+246x^124+96x^125+252x^127+960x^128+312x^129+252x^131+537x^132+156x^133+132x^135+264x^136+132x^137+84x^139+438x^140+36x^141+48x^143+111x^144+36x^145+3x^148

The gray image is a linear code over GF(4) with n=176, k=6 and d=124.
This code was found by Heurico 1.16 in 0.062 seconds.