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 1 1 1 X 1 1 1 X 1 X 1 1 1 0 X 0 0 0 0 X X 3X X X 4X 2X 4X X 4X 4X 4X 4X 5X 5X 3X 6X 0 3X 6X 4X 4X X X X 0 2X 0 3X 5X 6X 3X 0 6X 0 5X 0 X 3X 0 5X 5X 5X X 3X X 4X 4X 0 0 0 X 0 0 X 5X 5X 3X 4X 2X 4X X X 3X 2X 4X 5X 5X 6X 2X 4X 5X 5X 3X 3X 4X X 0 0 6X 4X 6X 5X 0 0 X 0 X 0 X X 5X 3X 5X X 4X 0 6X 2X 3X 4X 2X 5X 3X 0 0 0 X 0 5X 5X 6X 2X 2X 4X 4X 5X 0 6X 4X 0 4X 0 X 6X 3X 3X 2X X 0 2X 3X 3X 2X 3X 3X 3X 3X X 4X X 4X 2X 0 5X X 3X 3X 0 X 6X 4X 2X 0 X 3X 6X 6X 3X 0 0 0 0 X 5X 6X 2X 6X 5X 4X 5X 6X 6X 3X 0 2X 5X 4X 3X 2X X 4X 5X 4X 6X X 0 6X 0 0 3X 2X X 0 5X 6X 5X 5X X 0 0 5X 6X 6X 3X 5X X 2X 6X 2X 0 4X 0 6X generates a code of length 55 over Z7[X]/(X^2) who´s minimum homogenous weight is 294. Homogenous weight enumerator: w(x)=1x^0+348x^294+1134x^301+42x^306+1590x^308+1008x^313+1758x^315+9072x^320+2160x^322+36288x^327+2058x^329+54432x^334+2262x^336+2094x^343+1728x^350+1026x^357+486x^364+132x^371+30x^378 The gray image is a linear code over GF(7) with n=385, k=6 and d=294. This code was found by Heurico 1.16 in 11.9 seconds.