The generator matrix

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

generates a code of length 35 over Z2[X]/(X^2) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+41x^24+112x^25+218x^26+338x^27+462x^28+636x^29+725x^30+930x^31+1153x^32+1256x^33+1431x^34+1568x^35+1521x^36+1362x^37+1257x^38+1004x^39+742x^40+558x^41+391x^42+294x^43+165x^44+98x^45+70x^46+26x^47+11x^48+10x^49+4x^50

The gray image is a linear code over GF(2) with n=70, k=14 and d=24.
This code was found by an older version of Heurico in 0 seconds.