The generator matrix

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

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+86x^24+180x^25+447x^26+606x^27+854x^28+1178x^29+1435x^30+1878x^31+2225x^32+2658x^33+3057x^34+3154x^35+3106x^36+2952x^37+2446x^38+2008x^39+1466x^40+1068x^41+817x^42+494x^43+294x^44+142x^45+111x^46+50x^47+30x^48+14x^49+7x^50+2x^51+2x^52

The gray image is a linear code over GF(2) with n=70, k=15 and d=24.
This code was found by Heurico 1.16 in 57.1 seconds.