The generator matrix

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

generates a code of length 35 over Z2[X]/(X^2) who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+46x^29+98x^30+92x^31+108x^32+96x^33+69x^34+80x^35+74x^36+84x^37+46x^38+46x^39+65x^40+40x^41+41x^42+20x^43+8x^44+6x^45+2x^46+2x^47

The gray image is a linear code over GF(2) with n=70, k=10 and d=29.
This code was found by an older version of Heurico in 0 seconds.