The generator matrix

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

generates a code of length 35 over Z2[X]/(X^2) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+72x^27+144x^28+188x^29+273x^30+298x^31+287x^32+312x^33+287x^34+328x^35+368x^36+328x^37+323x^38+244x^39+220x^40+184x^41+105x^42+80x^43+35x^44+12x^45+4x^46+2x^47+1x^60

The gray image is a linear code over GF(2) with n=70, k=12 and d=27.
This code was found by Heurico 1.10 in 0.359 seconds.