The generator matrix

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

generates a code of length 42 over F4[X]/(X^2) who´s minimum homogenous weight is 118.

Homogenous weight enumerator: w(x)=1x^0+144x^118+60x^119+258x^120+408x^121+552x^122+132x^123+366x^124+324x^125+348x^126+84x^127+90x^128+252x^129+240x^130+60x^131+234x^132+60x^133+156x^134+48x^135+66x^136+108x^137+96x^138+9x^144

The gray image is a linear code over GF(4) with n=168, k=6 and d=118.
This code was found by Heurico 1.16 in 0.047 seconds.