The generator matrix 1 0 0 0 0 0 0 0 1 1 1 0 1 0 1 X 0 X 0 1 1 1 1 1 1 1 0 1 0 1 1 1 1 0 1 1 X X X X X X 1 1 1 X 1 1 1 0 0 1 0 1 1 0 0 0 0 1 1 1 0 X 0 1 0 1 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 1 1 X+1 1 1 X+1 X+1 1 1 1 1 1 0 X X+1 1 1 1 1 X X 1 X+1 1 0 1 1 1 X 0 X X+1 X+1 0 X 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 X 1 1 1 1 1 1 X X+1 1 X+1 X X 1 0 0 1 X+1 0 X X 0 0 X+1 X X+1 0 1 X X+1 X+1 1 X+1 1 0 1 1 X X+1 1 X+1 1 X+1 1 0 1 0 X+1 X+1 0 1 1 0 0 0 0 1 0 0 0 0 0 1 1 X 0 1 X 0 X+1 X+1 1 1 X+1 X 1 X+1 X+1 0 0 X+1 X 0 X+1 X X 0 1 X+1 1 X+1 X+1 X 1 1 1 X+1 X+1 1 0 X X X X+1 X+1 1 1 X 0 0 0 1 X X+1 X+1 1 X+1 0 0 0 0 0 0 1 0 0 0 1 0 X 1 X+1 0 0 X X+1 X+1 X+1 1 X X X+1 X+1 X+1 1 0 1 1 0 X 1 X+1 0 X X+1 X+1 1 0 1 1 X+1 X+1 1 0 1 0 1 X+1 1 0 0 X+1 1 0 0 X X X+1 0 X X+1 1 0 1 0 0 0 0 0 0 1 0 0 1 X X+1 X X+1 1 X+1 X+1 X X+1 X X+1 X+1 0 0 X 0 0 0 X 0 1 0 1 0 X X+1 0 1 X 0 0 X X+1 1 X+1 X+1 1 X X+1 X+1 X+1 X+1 1 0 0 X 0 1 1 1 0 1 0 1 X+1 0 0 0 0 0 0 0 0 1 0 1 X+1 0 1 X 1 1 X X+1 0 X X 0 X+1 X+1 0 X 1 1 1 0 0 0 X+1 0 0 1 X+1 X+1 X+1 1 0 0 X 1 1 X X X X+1 X X+1 X+1 1 X X+1 1 X 1 0 X+1 X+1 1 X 1 X+1 0 0 0 0 0 0 0 0 0 1 X 1 X 1 X+1 1 1 1 1 X+1 X X 1 0 X X+1 X 0 X+1 1 X+1 X X 0 1 1 0 0 0 X X X X 0 X+1 1 X 0 1 1 1 0 1 1 1 X+1 1 1 1 1 0 X 0 0 X X+1 0 0 generates a code of length 66 over Z2[X]/(X^2) who´s minimum homogenous weight is 50. Homogenous weight enumerator: w(x)=1x^0+76x^50+94x^51+321x^52+422x^53+716x^54+912x^55+1199x^56+1338x^57+1813x^58+2082x^59+2608x^60+3104x^61+3477x^62+3756x^63+3860x^64+4454x^65+4347x^66+4562x^67+4110x^68+4136x^69+3609x^70+3300x^71+2745x^72+2062x^73+1760x^74+1302x^75+1064x^76+736x^77+579x^78+348x^79+299x^80+114x^81+119x^82+24x^83+41x^84+18x^85+11x^86+4x^87+8x^88+5x^90 The gray image is a linear code over GF(2) with n=132, k=16 and d=50. This code was found by Heurico 1.11 in 237 seconds.