The generator matrix

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

generates a code of length 42 over F4[X]/(X^2) who´s minimum homogenous weight is 121.

Homogenous weight enumerator: w(x)=1x^0+156x^121+84x^122+120x^123+33x^124+216x^125+48x^126+18x^128+156x^129+36x^130+72x^131+24x^134+9x^136+48x^137+3x^148

The gray image is a linear code over GF(4) with n=168, k=5 and d=121.
This code was found by Heurico 1.16 in 0.016 seconds.