The generator matrix

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

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+111x^112+120x^113+216x^115+468x^116+528x^117+732x^119+630x^120+1056x^121+1296x^123+744x^124+1584x^125+2232x^127+1077x^128+1800x^129+1464x^131+642x^132+960x^133+204x^135+243x^136+96x^137+75x^140+57x^144+36x^148+9x^152+3x^156

The gray image is a linear code over GF(4) with n=168, k=7 and d=112.
This code was found by Heurico 1.16 in 0.873 seconds.