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 X 1 1 1 1 1 1 1 1 1 1 1 X 1 1 1 0 X 0 0 0 0 0 0 X X 3X X 3X 2X 5X X 2X 2X 4X 6X 6X 2X 2X 5X 6X 5X X 3X 2X 3X 0 6X 5X 3X 2X 4X 5X 5X 0 X 6X 6X 5X X 0 5X 2X 6X 2X 4X 2X 6X 3X 5X X 4X X 0 6X 0 2X X 0 X 2X 4X 2X 2X X 2X 0 0 0 0 X 0 0 X X 4X 5X 6X 2X 2X 5X X 6X X 3X 0 6X X 4X 6X 0 5X 2X 5X 6X 6X 0 5X 0 6X 2X X 2X 3X 6X 5X 3X 0 4X 0 5X 5X 3X 2X 4X 4X 5X X 4X 6X 2X 0 2X 6X 4X 4X 0 4X X 4X 5X 3X 2X 4X 6X 6X 0 6X 4X 0 0 0 0 X 0 5X 4X 3X 5X 4X 3X 6X 0 4X 6X 5X 5X 5X 5X 2X 0 6X X 2X 5X 0 3X 3X 3X 5X X 2X 6X 2X 6X 3X X 0 0 3X 5X 3X 6X 2X X X 2X 3X 2X 3X 3X 0 3X 0 3X 0 6X 5X 6X X X 0 0 2X 4X 2X 4X 6X 5X 2X 5X 3X 0 0 0 0 X 5X X 2X 2X 5X 5X 0 X 2X 0 3X 2X 6X 5X 6X 2X 4X 4X 2X 3X 6X 4X 3X 2X 2X 5X 3X 6X X 4X X 0 0 6X 4X 0 2X 3X 6X 0 4X 3X 2X 2X 5X 6X X 3X 5X X 0 5X 4X X 5X X 4X X 2X X 2X 6X 3X 3X 3X 3X 0 generates a code of length 72 over Z7[X]/(X^2) who´s minimum homogenous weight is 392. Homogenous weight enumerator: w(x)=1x^0+234x^392+936x^399+1554x^406+1770x^413+3822x^420+26580x^427+75936x^434+1836x^441+1698x^448+1374x^455+990x^462+618x^469+246x^476+30x^483+24x^490 The gray image is a linear code over GF(7) with n=504, k=6 and d=392. This code was found by Heurico 1.16 in 16.3 seconds.