The generator matrix 1 0 0 0 0 1 1 1 1 1 1 1 X X X 0 X 0 0 0 0 X 0 1 X 1 1 1 1 0 1 1 1 X 0 1 X 0 1 1 X 1 1 1 0 1 X 1 0 X X 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 1 0 0 1 1 0 1 1 1 1 1 0 0 X 1 1 1 0 X X 0 X X 1 0 X X X+1 1 1 X+1 X 1 X 0 0 X X 0 X 0 1 X+1 1 0 1 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 0 1 0 1 0 X+1 1 X X 1 X X X 1 1 X 0 X+1 0 X+1 0 1 X+1 X+1 0 X+1 X X X 1 0 1 X+1 0 X+1 1 X X+1 1 1 X X+1 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 0 1 1 0 0 X+1 1 0 X 0 X X X+1 1 1 0 0 1 X+1 1 X+1 1 X X+1 1 0 1 X X 1 X 0 0 0 1 1 0 X X+1 0 1 1 X 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 X 1 1 1 X X+1 1 X+1 X 0 1 1 X 0 X X+1 0 X 1 0 1 0 0 0 X X X 1 1 X+1 X+1 1 0 1 0 X+1 1 1 1 X X X+1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 0 X 0 X X 0 0 X X 0 X X X 0 0 0 0 X 0 0 X X 0 X X 0 0 0 0 X X 0 0 X X X X X X 0 0 X X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 X X X 0 0 X X X X 0 0 0 0 X 0 X 0 0 X X X X 0 0 X 0 0 0 X 0 0 X 0 0 X 0 0 X X 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 X 0 0 X 0 X 0 X 0 0 X X X 0 X X X X 0 0 X 0 X X X X 0 0 0 X 0 X X 0 X X X 0 X X 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 X 0 X 0 0 X X X X X X 0 0 0 0 X 0 X 0 0 0 X 0 X 0 X X 0 0 0 0 0 X X X 0 0 X X 0 X X 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 X 0 X X 0 X X X X 0 0 0 X 0 X X 0 0 0 0 0 X X 0 0 X 0 X X 0 0 0 X X X X X 0 X 0 0 X X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 generates a code of length 68 over Z2[X]/(X^2) who´s minimum homogenous weight is 40. Homogenous weight enumerator: w(x)=1x^0+64x^40+149x^42+261x^44+542x^46+842x^48+970x^50+1250x^52+1301x^54+1278x^56+1265x^58+1220x^60+1520x^62+1975x^64+2406x^66+2579x^68+2458x^70+2018x^72+1596x^74+1302x^76+1091x^78+1262x^80+1325x^82+1233x^84+1106x^86+756x^88+478x^90+293x^92+155x^94+44x^96+19x^98+6x^100+3x^102 The gray image is a linear code over GF(2) with n=136, k=15 and d=40. This code was found by Heurico 1.16 in 99.6 seconds.