The generator matrix 1 0 0 1 1 1 0 1 1 1 1 0 X 0 1 1 1 1 X 0 X 0 0 1 1 1 1 1 X 1 0 1 0 0 1 0 1 0 0 X 1 0 0 1 1 X X 1 1 1 1 1 0 1 1 0 1 1 1 0 1 1 1 0 1 X 1 1 0 1 0 1 0 1 1 0 0 1 1 1 1 X X+1 1 0 X 1 0 1 0 1 X 1 0 X+1 1 1 X+1 1 X+1 1 1 0 0 X+1 1 1 0 X 1 1 0 0 1 1 X+1 0 X X+1 0 1 X+1 1 1 X X X 1 X+1 X+1 1 1 0 1 X+1 0 0 0 1 1 1 0 1 0 1 1 0 X X+1 1 0 X+1 0 1 X+1 1 X 1 0 0 1 1 X X X+1 1 0 X+1 0 1 X 1 X X+1 X+1 1 0 X+1 X+1 1 X+1 0 0 1 X X+1 X X+1 0 0 1 1 X X+1 0 1 X 1 0 1 1 1 X 0 0 0 0 X 0 0 0 0 0 0 0 X X 0 X X X X X 0 0 0 X X 0 X X X 0 0 0 0 X X X 0 0 X 0 0 0 0 0 0 X 0 X X X 0 X 0 0 0 0 X X 0 X X 0 X X 0 0 X X 0 0 0 0 0 X 0 0 0 0 0 0 0 0 X 0 X X X 0 X X 0 X 0 0 0 X X X 0 0 0 X 0 0 0 0 0 X X X 0 X 0 X X 0 0 X X 0 X X 0 X 0 0 0 X 0 X X X 0 X X X 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 X 0 0 0 0 X X X 0 0 0 X X 0 0 0 X 0 0 X X X X X 0 0 X X X 0 X 0 X 0 0 X X 0 X 0 X 0 0 X 0 X X X 0 X 0 0 0 X 0 0 0 0 0 0 X 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 X 0 0 0 X X X X X 0 X X X 0 X X 0 X X 0 X X 0 X X 0 0 0 X 0 X 0 0 X 0 X 0 0 X 0 X 0 X 0 X X 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 X X 0 0 X X X X X 0 X 0 X X 0 X X 0 0 X 0 X X 0 X X 0 X 0 X X X 0 0 0 0 X X 0 0 X 0 0 0 0 X X 0 X 0 X 0 0 0 0 0 0 0 0 X 0 0 0 0 X 0 X X X 0 X X 0 X 0 0 X X X 0 X X X X X 0 X X X 0 0 X 0 0 0 0 0 0 X 0 0 X 0 0 0 0 0 X X 0 0 X X 0 0 X X 0 0 0 0 0 0 0 0 0 0 0 X 0 X X 0 X 0 X X X 0 0 0 X X X X X 0 0 0 X X 0 0 0 X 0 0 0 X 0 X 0 X 0 X X 0 X 0 0 X 0 X 0 0 0 X 0 0 X X X 0 0 X X 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 X X X 0 X X X 0 0 X X X 0 X 0 0 0 0 X X X 0 X 0 0 X X X X X 0 0 0 0 X 0 X 0 0 0 X 0 0 X X X X 0 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+116x^54+355x^56+578x^58+879x^60+1336x^62+1779x^64+2031x^66+2147x^68+2138x^70+1840x^72+1367x^74+863x^76+478x^78+272x^80+117x^82+45x^84+26x^86+9x^88+3x^90+2x^92+2x^94 The gray image is a linear code over GF(2) with n=136, k=14 and d=54. This code was found by Heurico 1.16 in 57.4 seconds.