The generator matrix

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

generates a code of length 42 over F4[X]/(X^2) who´s minimum homogenous weight is 108.

Homogenous weight enumerator: w(x)=1x^0+120x^108+252x^109+288x^110+1068x^111+1740x^112+2004x^113+1908x^114+4020x^115+4941x^116+5460x^117+4272x^118+9348x^119+9636x^120+10776x^121+8148x^122+17256x^123+17187x^124+18300x^125+11472x^126+23124x^127+20352x^128+18180x^129+10956x^130+18372x^131+13035x^132+10428x^133+5280x^134+6108x^135+4173x^136+2160x^137+684x^138+576x^139+411x^140+24x^141+39x^144+12x^148+27x^152+6x^156

The gray image is a linear code over GF(4) with n=168, k=9 and d=108.
This code was found by Heurico 1.16 in 138 seconds.