The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 X 1 0 X 0 0 0 0 X X X aX 0 X (a+1)X aX (a+1)X aX X X aX 0 (a+1)X X X (a+1)X 0 (a+1)X aX aX X 0 X aX aX aX 0 X X (a+1)X 0 aX X 0 X X 0 0 X 0 0 X (a+1)X aX aX aX 0 0 aX aX 0 aX (a+1)X aX (a+1)X (a+1)X aX 0 (a+1)X 0 (a+1)X (a+1)X X (a+1)X 0 (a+1)X 0 aX (a+1)X 0 (a+1)X X aX (a+1)X aX (a+1)X aX (a+1)X X aX 0 0 0 X 0 (a+1)X 0 X aX (a+1)X X X X 0 X (a+1)X X X (a+1)X (a+1)X (a+1)X 0 0 (a+1)X (a+1)X 0 aX 0 aX aX 0 X 0 aX X X (a+1)X (a+1)X X (a+1)X X (a+1)X (a+1)X aX 0 0 0 0 X X X (a+1)X X X X aX 0 0 0 aX X aX (a+1)X (a+1)X 0 X aX aX aX aX 0 X X 0 aX X aX 0 0 aX X 0 X 0 aX X X (a+1)X generates a code of length 44 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 120. Homogenous weight enumerator: w(x)=1x^0+270x^120+192x^126+312x^128+1152x^130+1728x^134+210x^136+138x^144+66x^152+21x^160+6x^168 The gray image is a linear code over GF(4) with n=176, k=6 and d=120. This code was found by Heurico 1.16 in 82 seconds.