The generator matrix

 1  0  0  1  1  1  1  1  1  1  1  1  1 (a+1)X  1  1  0  1  1  1  1  1  0  1  1  1  1  1  1  1  1 aX  1  1  1  1  1 (a+1)X  0  1  1  1
 0  1  0  0  0 (a+1)X  1 (a+1)X+a a+1 (a+1)X+1  1 (a+1)X+a  a  1 (a+1)X+a+1 (a+1)X+a+1  1 (a+1)X+1 a+1  a  X (a+1)X+1  1 X+a+1 (a+1)X X+a  1  a  a aX+1 (a+1)X+a+1  1 a+1 (a+1)X+a  0 aX+1 (a+1)X  1 (a+1)X a+1 aX  1
 0  0  1  1  a a+1  1 X+1  1  0 a+1 X+a+1  a X+1 aX+a aX  a  a a+1  X (a+1)X+a aX+a+1 aX+a+1 X+1  X X+1 X+a (a+1)X+a  X  0 (a+1)X+a (a+1)X+a+1 (a+1)X+a X+1 aX+1 X+1  a (a+1)X+1  1 X+a+1 X+a+1 (a+1)X+1
 0  0  0 (a+1)X  0  0  0 aX aX aX (a+1)X  X (a+1)X (a+1)X  X  X  X aX (a+1)X  X aX  X  0 aX aX  0  0  0  X (a+1)X  0  X aX  0  0 aX  X  X aX  0 aX  X
 0  0  0  0  X aX (a+1)X  X  0 aX  X (a+1)X aX (a+1)X  0  X  X  0 aX aX  X  X (a+1)X (a+1)X aX  X  X (a+1)X  0  0  0  0 aX aX (a+1)X  0 (a+1)X  X  0  0 aX 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+432x^112+804x^113+588x^114+1635x^116+2412x^117+1968x^118+3591x^120+4164x^121+3480x^122+4920x^124+5544x^125+5184x^126+6114x^128+6684x^129+5340x^130+4509x^132+4044x^133+1776x^134+1167x^136+924x^137+96x^138+45x^140+69x^144+24x^148+18x^152+3x^156

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 28 seconds.