The generator matrix

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

generates a code of length 43 over F4[X]/(X^2) who´s minimum homogenous weight is 124.

Homogenous weight enumerator: w(x)=1x^0+87x^124+144x^125+96x^126+213x^128+120x^129+72x^130+99x^132+108x^133+27x^136+24x^138+15x^140+12x^141+3x^144+3x^156

The gray image is a linear code over GF(4) with n=172, k=5 and d=124.
This code was found by Heurico 1.16 in 0.016 seconds.