The generator matrix

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

generates a code of length 35 over Z2[X]/(X^2) who´s minimum homogenous weight is 23.

Homogenous weight enumerator: w(x)=1x^0+72x^23+271x^24+446x^25+745x^26+1018x^27+1625x^28+2108x^29+3071x^30+3890x^31+4538x^32+5594x^33+5920x^34+6368x^35+6158x^36+5692x^37+4958x^38+3944x^39+2989x^40+2214x^41+1577x^42+1014x^43+625x^44+312x^45+227x^46+78x^47+49x^48+18x^49+14x^50

The gray image is a linear code over GF(2) with n=70, k=16 and d=23.
This code was found by Heurico 1.11 in 85.7 seconds.