The generator matrix

 1  0  0  0  0  0  1  1  1  X  1  1  X  1  0  0  1  1  0  X  0  1  1  1  X  0  0  X  1  0  0  1  1  1  1
 0  1  0  0  0  0  0  0  0  1  1 X+1  0 X+1  1  1 X+1  X  1  X  0  X  X  1  X  0  1  1  1  1  1  1  0  0  X
 0  0  1  0  0  0  0  0  0  0  1 X+1  1  X  0 X+1  X  1  1  0  X  0 X+1  1  1  0  X  0 X+1  X  1  X  0  0  X
 0  0  0  1  0  0  0  1  1  1  0 X+1 X+1  1  1 X+1  0  X X+1  1  1  1  1 X+1  1  1 X+1  X X+1  1  1 X+1 X+1 X+1  X
 0  0  0  0  1  0  1  1  0  1  0  1 X+1  X  X X+1  X X+1 X+1 X+1  1  X  X  0  1  0  0  1  X  1  X  X  X  X  1
 0  0  0  0  0  1  1  0  1  1  X X+1 X+1  1  1  X  1  0  1  0  1  X  X  1  X X+1  0 X+1  X X+1 X+1 X+1  1  0  0
 0  0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  0  0  X  X  0  X  X  0  X  X  0  0
 0  0  0  0  0  0  0  X  0  0  X  0  X  X  X  X  0  0  0  X  0  X  X  0  0  X  X  X  0  0  X  X  0  0  0
 0  0  0  0  0  0  0  0  X  0  0  X  X  0  X  X  X  X  X  0  X  X  0  0  X  X  X  0  X  0  0  0  0  0  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+122x^24+178x^25+377x^26+602x^27+804x^28+1178x^29+1536x^30+1918x^31+2349x^32+2626x^33+2938x^34+3106x^35+3005x^36+3024x^37+2442x^38+2000x^39+1578x^40+1026x^41+813x^42+514x^43+294x^44+150x^45+76x^46+50x^47+38x^48+10x^49+8x^50+2x^51+1x^52+2x^54

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 71.2 seconds.