The generator matrix

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

generates a code of length 42 over F4[X]/(X^2) who´s minimum homogenous weight is 112.

Homogenous weight enumerator: w(x)=1x^0+339x^112+324x^113+648x^114+1020x^115+1512x^116+1296x^117+1944x^118+2352x^119+3045x^120+2304x^121+2868x^122+3468x^123+4242x^124+3540x^125+3780x^126+4572x^127+5085x^128+3816x^129+3924x^130+4032x^131+4065x^132+2124x^133+1812x^134+1380x^135+1068x^136+420x^137+384x^138+72x^139+84x^140+3x^144+9x^148+3x^152

The gray image is a linear code over GF(4) with n=168, k=8 and d=112.
This code was found by Heurico 1.16 in 10.2 seconds.