The generator matrix 1 0 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 X 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 (a+1)X X 1 1 1 1 1 1 (a+1)X 1 X 1 1 (a+1)X 1 1 1 1 1 1 1 1 1 1 0 (a+1)X X (a+1)X 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 X 1 1 1 aX 1 (a+1)X 1 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 (a+1)X+a+1 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 (a+1)X+1 X+a X X+a aX+a+1 aX 1 X+1 1 (a+1)X+a aX+a+1 1 aX+a+1 (a+1)X+1 X+a+1 aX+a X+a aX X+a X+1 aX+1 aX+1 1 1 1 1 X+1 aX+a X X+a (a+1)X+a X+a+1 (a+1)X+a+1 X+a 1 X+1 1 1 aX+a X a a (a+1)X+a 1 (a+1)X a (a+1)X+1 1 1 1 a 0 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 aX (a+1)X aX (a+1)X (a+1)X aX aX 0 X X 0 aX X aX X aX aX 0 (a+1)X aX (a+1)X aX (a+1)X aX (a+1)X (a+1)X aX (a+1)X (a+1)X aX 0 X (a+1)X (a+1)X X 0 X aX 0 0 0 0 aX X X 0 0 (a+1)X 0 0 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 (a+1)X 0 (a+1)X 0 0 X (a+1)X (a+1)X X aX (a+1)X (a+1)X X (a+1)X (a+1)X 0 0 X (a+1)X aX 0 X X (a+1)X 0 (a+1)X (a+1)X X X aX (a+1)X (a+1)X X aX (a+1)X aX (a+1)X X (a+1)X aX X (a+1)X X 0 (a+1)X 0 aX X 0 X 0 (a+1)X 0 0 aX aX 0 X (a+1)X 0 0 aX X 0 0 aX 0 (a+1)X (a+1)X (a+1)X X 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 X (a+1)X X aX X (a+1)X 0 (a+1)X aX X 0 0 X aX (a+1)X (a+1)X aX (a+1)X aX (a+1)X 0 aX X X X 0 aX 0 X 0 X (a+1)X (a+1)X 0 (a+1)X 0 (a+1)X (a+1)X X aX X aX 0 aX X 0 X aX 0 X (a+1)X 0 X 0 X (a+1)X (a+1)X aX 0 aX 0 X X aX X aX (a+1)X 0 (a+1)X X 0 generates a code of length 87 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 244. Homogenous weight enumerator: w(x)=1x^0+78x^244+492x^247+339x^248+1440x^251+585x^252+1944x^255+639x^256+2088x^259+690x^260+2364x^263+690x^264+2268x^267+414x^268+1296x^271+384x^272+336x^275+153x^276+48x^279+39x^280+12x^283+15x^284+9x^288+18x^292+15x^296+9x^300+6x^304+3x^308+3x^312+3x^316+3x^320 The gray image is a linear code over GF(4) with n=348, k=7 and d=244. This code was found by Heurico 1.16 in 2.06 seconds.