The generator matrix 1 0 0 0 0 0 0 1 1 1 X 1 1 0 1 0 1 X 0 1 1 1 1 0 1 1 X 0 1 X 1 X 0 X 1 X 1 1 0 1 1 0 0 1 1 1 1 0 1 X 1 0 X X 1 0 1 X 1 X 0 0 X X 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X X X 0 0 0 0 0 0 0 X X X X X 0 X X X X 1 X+1 X+1 1 1 X+1 1 1 X+1 1 X+1 1 X+1 1 1 1 1 1 1 1 0 1 1 X 1 1 X X+1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 X X X X 0 0 1 X+1 X+1 1 1 X+1 1 1 1 1 1 1 X 1 X 1 X X+1 0 X X+1 1 X+1 X X+1 X+1 X+1 X+1 0 0 0 0 0 X+1 X+1 X+1 1 1 X+1 X+1 0 1 1 X 0 X 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 1 1 X+1 1 0 1 X 1 1 1 X X+1 1 X 0 X+1 X+1 1 X X 0 1 X+1 1 1 0 X 0 0 X X X 1 0 X 1 X+1 X+1 X 1 X 1 X 1 X X+1 X X+1 1 0 X X+1 1 1 0 0 0 0 1 0 0 0 1 1 1 0 X X 1 X+1 X+1 X+1 1 X 1 X+1 X 0 0 X+1 X+1 X+1 X X 0 X 1 1 X+1 1 0 0 0 0 X+1 X+1 X+1 0 X X 0 1 X+1 X+1 X+1 0 X+1 X 1 X X 1 0 X+1 X X+1 X+1 0 1 X+1 X 1 0 0 0 0 0 1 0 1 0 X+1 1 1 0 X+1 0 0 X+1 X+1 1 0 0 X+1 1 X X+1 0 X+1 1 X X+1 0 1 X 0 X+1 X+1 X 0 X X+1 X X+1 1 X 1 X+1 X+1 0 1 X+1 X+1 0 X 1 0 X+1 0 0 X X 1 X+1 X 0 0 1 0 0 0 0 0 0 0 0 1 1 X+1 X 1 X 1 1 0 1 1 0 0 0 0 0 1 1 X X+1 1 0 1 X 0 1 X+1 X+1 1 0 1 X 0 X+1 X+1 X X+1 X+1 X 1 0 X 1 X+1 1 X+1 1 1 X 1 1 0 0 X+1 0 0 0 X 1 1 1 1 0 0 0 0 0 0 0 X X 0 0 0 0 X 0 X 0 0 X X 0 X X 0 0 0 X X 0 0 X X X 0 X X 0 0 X 0 0 0 X X X 0 0 0 0 X 0 X 0 0 X X 0 0 X X X 0 0 X 0 X 0 X generates a code of length 68 over Z2[X]/(X^2) who´s minimum homogenous weight is 54. Homogenous weight enumerator: w(x)=1x^0+163x^54+694x^56+1322x^58+1948x^60+2608x^62+3390x^64+4051x^66+4134x^68+4262x^70+3569x^72+2807x^74+1906x^76+1052x^78+534x^80+213x^82+66x^84+27x^86+11x^88+7x^90+2x^92+1x^96 The gray image is a linear code over GF(2) with n=136, k=15 and d=54. This code was found by Heurico 1.11 in 58.5 seconds.