The generator matrix 1 0 1 1 1 1 1 1 1 0 1 1 1 0 1 1 X 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 (a+1)X X 1 1 1 1 0 1 1 (a+1)X 1 1 aX 1 1 aX 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 (a+1)X 1 1 1 (a+1)X 1 1 0 X 1 0 1 1 a a+1 0 (a+1)X+1 (a+1)X+a+1 a 1 0 (a+1)X+1 (a+1)X+a+1 1 a X 1 (a+1)X+a+1 (a+1)X+1 a aX+a+1 0 aX+1 1 a (a+1)X+a+1 aX+1 (a+1)X+a+1 0 X+a aX+a+1 (a+1)X 1 1 1 X+a+1 X+a X (a+1)X+1 1 X+1 X+a 1 aX+a X+1 1 (a+1)X+1 aX+a 1 aX+a 1 X+a X (a+1)X+1 (a+1)X+1 X+a+1 aX+a X a+1 X X+a+1 aX aX X+a+1 (a+1)X+1 X+a a+1 X+1 X+1 a+1 X+a+1 X+a+1 1 (a+1)X 0 X+1 1 aX aX+1 X X (a+1)X+a+1 0 0 (a+1)X 0 0 0 X aX X X X (a+1)X (a+1)X aX aX aX 0 0 X aX (a+1)X aX (a+1)X (a+1)X (a+1)X aX X aX X aX (a+1)X X X aX aX 0 (a+1)X aX 0 (a+1)X aX (a+1)X 0 X 0 aX aX X (a+1)X (a+1)X (a+1)X 0 (a+1)X aX aX X X aX 0 (a+1)X X aX (a+1)X X X (a+1)X X (a+1)X X 0 aX aX X aX X 0 0 aX X X X 0 0 0 0 X 0 X (a+1)X (a+1)X X (a+1)X 0 (a+1)X X X 0 X 0 (a+1)X (a+1)X 0 0 X (a+1)X (a+1)X X (a+1)X (a+1)X aX X (a+1)X (a+1)X 0 0 X (a+1)X (a+1)X 0 X aX (a+1)X 0 X aX X (a+1)X (a+1)X X aX X X 0 0 0 aX X aX (a+1)X 0 0 X (a+1)X aX (a+1)X X aX aX aX 0 0 aX X 0 0 0 X (a+1)X X aX X (a+1)X (a+1)X 0 0 0 0 0 (a+1)X (a+1)X (a+1)X (a+1)X 0 aX X aX 0 aX (a+1)X X (a+1)X X X aX X (a+1)X 0 (a+1)X aX 0 0 X X aX (a+1)X (a+1)X aX (a+1)X aX aX 0 aX aX 0 0 (a+1)X (a+1)X aX (a+1)X (a+1)X (a+1)X 0 X X aX aX aX (a+1)X 0 (a+1)X X (a+1)X 0 aX 0 aX X 0 (a+1)X 0 0 (a+1)X (a+1)X (a+1)X X 0 aX aX 0 aX X (a+1)X aX 0 X aX generates a code of length 82 over F4[X,sigma]/(X^2) who�s minimum homogenous weight is 230. Homogenous weight enumerator: w(x)=1x^0+312x^230+276x^232+900x^234+585x^236+1464x^238+663x^240+2328x^242+615x^244+2136x^246+603x^248+2340x^250+717x^252+1752x^254+330x^256+864x^258+138x^260+192x^262+66x^264+18x^268+21x^272+18x^276+15x^280+12x^284+9x^288+9x^292 The gray image is a linear code over GF(4) with n=328, k=7 and d=230. This code was found by Heurico 1.16 in 16.1 seconds.