The generator matrix

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

generates a code of length 42 over F4[X]/(X^2) who´s minimum homogenous weight is 111.

Homogenous weight enumerator: w(x)=1x^0+156x^111+387x^112+336x^113+444x^114+1596x^115+1428x^116+840x^117+756x^118+3612x^119+2958x^120+1512x^121+1824x^122+5376x^123+4443x^124+2256x^125+2712x^126+8292x^127+5400x^128+2400x^129+2412x^130+6252x^131+3540x^132+1512x^133+948x^134+2244x^135+1131x^136+360x^137+120x^138+120x^139+66x^140+48x^144+24x^148+27x^152+3x^156

The gray image is a linear code over GF(4) with n=168, k=8 and d=111.
This code was found by Heurico 1.16 in 11.3 seconds.