The generator matrix
1 0 0 0 1 1 1 X 0 0 0 1 1 1 1 0 X 1 1 1 0 1 X 0 0 1 1 1 X 1 1 X 1 1 0 1 X 0 1 1 1 1 0 1 X 0 X 0 1 X 0 1 1 1 X 1 1 1 1 1 X X 1 1 1 1 1 X 0 1 1 1 X 1 1 1 1 0 1 X 0 1 X
0 1 0 0 0 0 0 0 1 1 1 1 X+1 1 1 X 1 1 X 1 X X 0 1 1 X+1 0 X 0 X+1 X 1 X 0 1 1 1 X 1 0 1 1 1 X+1 1 X 1 0 X 1 1 0 1 X+1 1 1 0 X X X 1 X 1 X+1 X 0 X 1 X 0 X+1 X+1 X X+1 1 X X 1 X 1 1 1 0
0 0 1 0 0 1 1 1 X 1 X+1 1 1 X 0 0 X 0 X+1 X+1 1 1 1 X 1 0 X 0 1 1 X+1 1 X+1 0 0 X+1 X+1 1 X 1 X 1 X+1 0 X X X+1 X 0 1 0 X+1 1 X 1 1 X+1 X 1 X+1 0 1 X X 0 X+1 X X 1 X+1 1 1 1 1 X+1 1 X+1 1 0 1 X X+1 0
0 0 0 1 1 1 0 1 1 X+1 X 0 1 X+1 X 1 1 1 X 0 X X+1 1 X X 0 1 0 1 X+1 0 X+1 X X+1 1 0 X 0 0 X+1 X X+1 1 0 X+1 1 0 1 X+1 1 X X+1 X+1 X 1 X X 0 X X+1 X+1 X X+1 1 X+1 0 1 1 1 1 1 0 0 X+1 0 X+1 0 X+1 X+1 1 0 X+1 0
0 0 0 0 X 0 0 0 0 0 0 X X X X X X 0 0 0 X X X 0 X X X 0 X X X 0 0 0 0 0 X X X X X X X 0 0 0 0 0 X X X 0 0 0 0 0 0 0 X X X X X X 0 X 0 0 0 0 X 0 0 0 X 0 0 0 X 0 X 0 X
0 0 0 0 0 X 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 0 X 0 X 0 0 X X X 0 0 X X 0 0 X 0 0 X 0 X X 0 X 0 X X 0 X 0 X 0 X X 0 0 X X X X X X X X X 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 0 X X X X X X X X X X X X X X X X X X 0 X X X X X X X 0 X X X X 0 X X 0 X 0 0 X 0 X X 0 X 0 X 0 0
generates a code of length 83 over Z2[X]/(X^2) who´s minimum homogenous weight is 74.
Homogenous weight enumerator: w(x)=1x^0+128x^74+203x^76+287x^78+299x^80+226x^82+231x^84+175x^86+137x^88+107x^90+82x^92+68x^94+53x^96+27x^98+16x^100+2x^102+2x^104+4x^106
The gray image is a linear code over GF(2) with n=166, k=11 and d=74.
This code was found by Heurico 1.16 in 0.835 seconds.