The generator matrix

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

generates a code of length 42 over F4[X]/(X^2) who´s minimum homogenous weight is 117.

Homogenous weight enumerator: w(x)=1x^0+96x^117+324x^118+96x^120+360x^121+588x^122+84x^124+360x^125+516x^126+12x^128+504x^129+564x^130+216x^133+264x^134+45x^136+48x^138+6x^140+3x^144+3x^152+6x^156

The gray image is a linear code over GF(4) with n=168, k=6 and d=117.
This code was found by Heurico 1.16 in 11 seconds.