The generator matrix

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

generates a code of length 42 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 117.

Homogenous weight enumerator: w(x)=1x^0+84x^117+336x^118+96x^120+420x^121+528x^122+84x^124+252x^125+624x^126+12x^128+588x^129+480x^130+192x^133+288x^134+45x^136+48x^138+6x^140+3x^144+3x^152+6x^156

The gray image is a linear code over GF(4) with n=168, k=6 and d=117.
This code was found by Heurico 1.16 in 10.7 seconds.