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.