The generator matrix

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

generates a code of length 42 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 118.

Homogenous weight enumerator: w(x)=1x^0+156x^118+96x^119+111x^120+576x^121+456x^122+192x^123+171x^124+540x^125+336x^126+120x^127+312x^129+132x^130+96x^131+150x^132+204x^133+156x^134+72x^135+6x^136+96x^137+108x^138+6x^144+3x^148

The gray image is a linear code over GF(4) with n=168, k=6 and d=118.
This code was found by Heurico 1.16 in 0.041 seconds.