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 X 1 X 1 1 1 1 1 X X 1 1 1 1 1 1 X X 1 1 1 1 X 0 X 0 0 0 0 0 0 0 0 0 aX (a+1)X aX X aX (a+1)X aX X 0 aX 0 aX X X (a+1)X aX aX (a+1)X 0 X aX (a+1)X X aX aX (a+1)X aX (a+1)X X aX 0 0 (a+1)X aX 0 (a+1)X aX aX X 0 0 aX 0 X X (a+1)X X 0 X X aX 0 aX aX X X X aX (a+1)X X X (a+1)X (a+1)X X X 0 (a+1)X aX aX X 0 0 X 0 0 0 0 X X X aX 0 aX aX aX (a+1)X 0 (a+1)X (a+1)X X X aX 0 X 0 aX aX X (a+1)X X 0 (a+1)X (a+1)X aX X 0 0 0 X X aX 0 X X aX aX X (a+1)X (a+1)X (a+1)X aX 0 0 (a+1)X (a+1)X (a+1)X (a+1)X X 0 X aX (a+1)X X aX X (a+1)X X X 0 X aX 0 (a+1)X (a+1)X aX 0 0 X 0 X aX 0 0 0 X 0 0 X (a+1)X aX aX aX 0 (a+1)X aX aX X (a+1)X aX aX 0 (a+1)X X (a+1)X X aX X 0 X 0 aX X X X 0 0 X (a+1)X (a+1)X aX aX X 0 0 (a+1)X 0 X (a+1)X (a+1)X 0 (a+1)X aX X X (a+1)X (a+1)X X aX (a+1)X 0 0 0 (a+1)X aX (a+1)X (a+1)X X (a+1)X X aX aX 0 0 X aX aX 0 (a+1)X 0 0 0 0 0 0 0 0 X 0 (a+1)X 0 X aX (a+1)X (a+1)X X 0 0 aX 0 aX 0 X aX X 0 aX X aX X aX 0 X aX (a+1)X (a+1)X (a+1)X X aX aX X 0 (a+1)X X aX X aX (a+1)X (a+1)X X (a+1)X 0 aX (a+1)X 0 X aX aX 0 aX aX X X 0 aX aX 0 0 0 0 0 0 X (a+1)X X 0 X aX (a+1)X (a+1)X 0 aX (a+1)X 0 0 0 0 0 0 X X X (a+1)X X X aX X 0 aX (a+1)X (a+1)X aX aX aX aX (a+1)X X aX aX aX X aX aX aX (a+1)X (a+1)X 0 0 (a+1)X 0 X 0 0 0 X X 0 (a+1)X aX X aX 0 aX 0 aX X (a+1)X 0 aX 0 (a+1)X (a+1)X (a+1)X 0 0 aX aX aX aX X X 0 (a+1)X X X aX (a+1)X (a+1)X aX X aX 0 X 0 (a+1)X generates a code of length 81 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 220. Homogenous weight enumerator: w(x)=1x^0+174x^220+345x^224+24x^226+417x^228+132x^230+429x^232+660x^234+417x^236+2280x^238+378x^240+3648x^242+333x^244+3924x^246+351x^248+1620x^250+237x^252+276x^256+198x^260+156x^264+168x^268+96x^272+60x^276+33x^280+12x^284+12x^288+3x^296 The gray image is a linear code over GF(4) with n=324, k=7 and d=220. This code was found by Heurico 1.16 in 3.96 seconds.