The generator matrix

1 0 0 0 0 1 1 1 0 1 1 0 X X 1 1 1 1 X 0 X 1 1 1 1 1 1 0 X X 1 1 0 X 1 0 0 0 1 X 1 X 1 1 X 1 X 1 0 0 1 0 1 0 X 0 0 1 1 1 1 1 X X 1 1 0 1 1 X 1 0 1 1 1
0 1 0 0 0 0 0 X 0 1 X+1 1 1 1 X+1 1 X 1 1 1 0 X 1 X+1 0 X+1 X 1 0 X 1 X X X X+1 X 1 0 1 1 0 X 0 X 0 X+1 0 X 1 1 1 1 1 X 1 0 1 0 X X+1 1 X X 1 X+1 X 1 X+1 1 1 0 1 X X+1 0
0 0 1 0 0 0 1 1 1 1 X X+1 0 1 0 X+1 0 1 X+1 X 1 X 0 X 1 1 X+1 X 1 1 0 X 1 1 X 0 X+1 X 1 0 0 0 0 1 1 X+1 X X+1 0 X+1 X X+1 X 1 X X X 1 0 X+1 1 X+1 X X+1 1 X+1 0 X+1 1 0 X+1 X+1 0 0 0
0 0 0 1 0 1 X X+1 1 X 1 1 1 X X X+1 0 0 0 X+1 1 1 0 X+1 X+1 1 X X X+1 0 X+1 X+1 0 X+1 0 1 1 0 1 1 0 X X+1 1 X 0 1 X X+1 X+1 X X X+1 1 0 X 0 1 0 1 0 0 1 X+1 X X+1 X X X X X+1 0 X X+1 0
0 0 0 0 1 X 0 0 X X 0 X 0 0 X X 1 1 1 1 1 1 X+1 1 X+1 1 X+1 X+1 1 1 1 X+1 X X X X 0 1 0 1 1 1 0 X+1 X X+1 X+1 X X+1 1 0 0 X+1 1 X+1 1 0 X+1 0 1 X 1 0 X+1 1 0 X 1 1 X+1 1 X+1 1 1 X

generates a code of length 75 over Z2[X]/(X^2) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+91x^68+182x^70+199x^72+134x^74+108x^76+72x^78+78x^80+56x^82+41x^84+18x^86+19x^88+12x^90+4x^92+4x^94+3x^96+2x^98

The gray image is a linear code over GF(2) with n=150, k=10 and d=68.
This code was found by Heurico 1.10 in 0.079 seconds.