The generator matrix

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

generates a code of length 43 over F4[X]/(X^2) who´s minimum homogenous weight is 120.

Homogenous weight enumerator: w(x)=1x^0+186x^120+96x^121+240x^123+687x^124+192x^125+192x^127+597x^128+192x^129+96x^131+591x^132+192x^133+192x^135+402x^136+96x^137+48x^139+72x^140+6x^144+15x^148+3x^156

The gray image is a linear code over GF(4) with n=172, k=6 and d=120.
This code was found by Heurico 1.16 in 0.0629 seconds.