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 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 1 1 1 1 1 1 1 X X 1 1 X 1 X 1 1 1 X X 0 X 0 0 0 0 X X X aX 0 X (a+1)X X (a+1)X (a+1)X (a+1)X aX X (a+1)X 0 (a+1)X aX X 0 aX X 0 0 (a+1)X (a+1)X (a+1)X (a+1)X 0 aX aX aX 0 (a+1)X aX aX 0 aX (a+1)X 0 aX X X 0 X X X aX X 0 X X (a+1)X (a+1)X X 0 aX aX (a+1)X (a+1)X aX aX aX (a+1)X (a+1)X X aX (a+1)X 0 (a+1)X 0 aX aX 0 (a+1)X X (a+1)X X X X (a+1)X X (a+1)X X X 0 aX 0 0 0 0 X 0 0 X (a+1)X aX aX aX 0 0 aX X 0 0 (a+1)X 0 aX aX aX aX (a+1)X (a+1)X X X 0 (a+1)X X (a+1)X 0 (a+1)X aX aX X 0 0 (a+1)X 0 0 aX aX X aX X X X X aX (a+1)X aX (a+1)X (a+1)X aX aX X X 0 aX 0 (a+1)X X (a+1)X X X (a+1)X aX aX X X 0 aX aX X X X 0 0 aX 0 X 0 X (a+1)X aX X X X aX X aX X aX 0 0 0 0 X 0 (a+1)X 0 X aX (a+1)X X X X X 0 aX 0 aX 0 (a+1)X (a+1)X X X (a+1)X (a+1)X (a+1)X aX (a+1)X 0 aX aX aX (a+1)X aX X (a+1)X X X (a+1)X (a+1)X aX 0 (a+1)X 0 aX X X 0 aX 0 aX aX aX 0 X X aX (a+1)X 0 X (a+1)X aX X (a+1)X aX (a+1)X X aX 0 0 aX (a+1)X (a+1)X aX (a+1)X X 0 aX 0 X (a+1)X 0 (a+1)X aX (a+1)X (a+1)X (a+1)X aX (a+1)X aX (a+1)X aX (a+1)X X 0 0 0 0 X X X (a+1)X X X X aX 0 aX X (a+1)X (a+1)X aX aX 0 aX (a+1)X (a+1)X (a+1)X (a+1)X (a+1)X aX aX aX 0 0 X X aX (a+1)X X X 0 aX aX (a+1)X X X X aX 0 (a+1)X 0 (a+1)X (a+1)X 0 aX 0 (a+1)X (a+1)X X 0 0 aX 0 0 0 X (a+1)X (a+1)X (a+1)X 0 aX aX X 0 0 aX (a+1)X X 0 X 0 (a+1)X aX 0 aX aX 0 (a+1)X aX X X (a+1)X aX X (a+1)X 0 (a+1)X generates a code of length 94 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 268. Homogenous weight enumerator: w(x)=1x^0+186x^268+24x^269+150x^272+240x^273+162x^276+480x^277+117x^280+912x^281+126x^284+1032x^285+66x^288+384x^289+48x^292+48x^296+15x^300+18x^304+9x^308+33x^312+18x^316+6x^320+9x^324+3x^328+3x^336+3x^344+3x^348 The gray image is a linear code over GF(4) with n=376, k=6 and d=268. This code was found by Heurico 1.16 in 3.73 seconds.