The generator matrix

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

generates a code of length 43 over F4[X]/(X^2) who´s minimum homogenous weight is 121.

Homogenous weight enumerator: w(x)=1x^0+228x^121+108x^122+204x^123+165x^124+696x^125+72x^126+516x^127+273x^128+348x^129+72x^130+180x^131+99x^132+228x^133+72x^134+156x^135+54x^136+336x^137+60x^138+96x^139+45x^140+84x^141+3x^148

The gray image is a linear code over GF(4) with n=172, k=6 and d=121.
This code was found by Heurico 1.16 in 0.047 seconds.