The generator matrix 1 0 0 0 1 1 1 0 1 1 1 1 X X 0 1 1 1 1 0 1 X 1 1 X X 0 0 1 1 0 0 1 1 X 0 1 X X X 0 1 X X 0 1 1 1 1 1 1 1 1 1 X 0 1 1 1 1 1 X 1 1 X X 1 0 1 0 0 0 1 1 1 0 0 X+1 X+1 1 X 1 X X+1 0 1 1 0 1 X 0 X 1 1 0 X+1 X+1 1 1 1 X X 1 X+1 0 X 1 1 1 1 0 1 0 0 X 0 X+1 X+1 1 X+1 0 0 0 X 0 1 0 X+1 X 0 X+1 1 X X 0 0 1 0 1 1 0 1 0 1 1 0 0 1 X+1 X+1 X 0 1 X+1 X+1 X 0 0 1 X X 0 0 1 0 1 X X+1 1 0 X+1 1 0 X X+1 X 1 1 X+1 0 X+1 X 1 X 1 X 0 X 1 1 1 X 1 X 1 1 X+1 X+1 X+1 1 X 0 0 0 1 1 0 1 1 1 0 1 X 1 1 0 X 1 X+1 X X+1 1 1 0 X+1 0 X 0 1 X+1 1 0 0 0 1 1 1 X 1 1 X+1 1 X X+1 0 1 X+1 X 0 X+1 X+1 1 0 1 0 0 1 X+1 X+1 X+1 0 0 X 1 1 X 1 X 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 X X X X X X 0 0 X X 0 X 0 X X X X X 0 0 X X X X X 0 0 X X X 0 X 0 0 0 0 0 0 X 0 0 0 0 X X X 0 X 0 0 0 0 0 0 X 0 0 0 0 0 0 X 0 0 0 X X 0 X X X 0 0 X X X X X X X X 0 X X X X 0 X 0 0 X 0 X X X 0 0 0 0 X X X 0 X 0 0 0 0 0 0 X 0 0 0 X 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X X X X X X X X X X X X X X X X X X X 0 0 X X 0 X 0 X X X X X 0 X 0 0 0 0 0 0 0 X 0 0 X X 0 0 X 0 0 X X 0 X 0 0 0 X X X 0 X 0 X 0 0 0 0 X X 0 X 0 X 0 0 X X X 0 0 0 0 X 0 0 X 0 X 0 X 0 X 0 X X X 0 0 0 0 0 0 0 0 0 0 0 X 0 X 0 0 0 0 X 0 0 0 0 X X X 0 X X 0 X X 0 0 X 0 X X 0 X 0 0 0 X X X 0 X 0 X X X 0 0 X X 0 0 0 0 0 0 X 0 0 X X X 0 0 0 0 0 0 0 0 0 0 0 X 0 X X X X 0 0 X 0 0 X 0 X X X X 0 X X X 0 0 0 X 0 X X X 0 X X 0 X 0 X X 0 X 0 0 0 0 X 0 0 0 X X 0 X 0 X 0 X X X 0 generates a code of length 67 over Z2[X]/(X^2) who´s minimum homogenous weight is 54. Homogenous weight enumerator: w(x)=1x^0+150x^54+465x^56+838x^58+1301x^60+1512x^62+1759x^64+2140x^66+2044x^68+1970x^70+1704x^72+1122x^74+754x^76+380x^78+148x^80+75x^82+12x^84+4x^86+3x^88+1x^92+1x^114 The gray image is a linear code over GF(2) with n=134, k=14 and d=54. This code was found by Heurico 1.16 in 82.2 seconds.