The generator matrix

 1  0  0  0  1  1  1  X  1 aX  1  1  X  1  1  0  1  1  1  1  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 (a+1)X  1  1  1  1  1
 0  1  0  0  X  1 X+1  1 (a+1)X  1 (a+1)X+1  0  1 X+1 aX+1  1 aX+a a+1 (a+1)X+a+1 aX+1  1 (a+1)X+a aX+a+1 (a+1)X (a+1)X+a+1  0 aX+1  a (a+1)X+a aX+a aX (a+1)X+a  a X+a+1 a+1  1 (a+1)X X+1 aX+a+1  0  a (a+1)X
 0  0  1  0 (a+1)X+1  1 (a+1)X (a+1)X+1 aX+1  a aX (a+1)X+a aX+1 a+1  a a+1  0  X (a+1)X aX+a+1 aX+a+1 aX+1 (a+1)X+1 (a+1)X+a+1 (a+1)X+1 aX+1 X+a+1 X+1 a+1 aX+a (a+1)X X+1 X+a+1 a+1 aX+a (a+1)X+1  1  1  X aX (a+1)X+a  1
 0  0  0  1 a+1  X aX+a+1 aX+a+1  a aX (a+1)X+a aX (a+1)X+a (a+1)X  1 (a+1)X+1 X+1 X+a (a+1)X aX+a X+a (a+1)X aX+1 a+1  a aX+1 (a+1)X+1 X+a aX+a+1 aX+a (a+1)X+a X+a+1  X aX (a+1)X+a (a+1)X+1  a a+1 (a+1)X+a+1 X+1 X+1 aX

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

Homogenous weight enumerator: w(x)=1x^0+291x^112+456x^113+612x^114+612x^115+1500x^116+2100x^117+1956x^118+1680x^119+2841x^120+3084x^121+2952x^122+2076x^123+4539x^124+5208x^125+3804x^126+2856x^127+5307x^128+5232x^129+3768x^130+2532x^131+3906x^132+3252x^133+1872x^134+936x^135+948x^136+636x^137+396x^138+60x^139+111x^140+9x^144+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 11.5 seconds.