The generator matrix

 1  0  0  0  0  0  0  1  1  1  1  1  1  X  1  X  X  X  0  X  1  X  1  1  1  0  X  1  0  1  X  0  1  1  1
 0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  1  1  1 X+1  X X+1  X X+1  X  1  X  1 X+1  1  1  X  0  X
 0  0  1  0  0  0  0  0  0  1  1  X X+1  1 X+1  1  1  X  0  0  X  1  X  X X+1  X X+1  0  1  X  0  0  1 X+1  0
 0  0  0  1  0  0  0  0  1  0  X X+1  1  1 X+1  X  1  1  1  1  0  X  X  1  1  1  1  1  X  X  X  X  0 X+1  0
 0  0  0  0  1  0  0  0  1  1  0 X+1  0 X+1 X+1  X  0  X X+1  0  1 X+1 X+1  X  X  0  X  X  1  1  0  X  0  0  0
 0  0  0  0  0  1  0  1  0 X+1  X  X X+1  0  X  1 X+1  0 X+1  1  X  X X+1  0  1  1  1  0  1 X+1  0 X+1 X+1  X  0
 0  0  0  0  0  0  1  1 X+1  X X+1  X  X  1  X X+1  0  X  X X+1  1  X X+1 X+1  1  0  0  X  0 X+1 X+1  1  1  1  0
 0  0  0  0  0  0  0  X  X  0  X  0  0  0  X  0  X  X  X  0  X  X  0  X  0  X  0  X  X  X  X  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+114x^24+156x^25+383x^26+624x^27+949x^28+1106x^29+1455x^30+1906x^31+2264x^32+2626x^33+2924x^34+3304x^35+3018x^36+2936x^37+2504x^38+1988x^39+1494x^40+1084x^41+801x^42+456x^43+311x^44+150x^45+113x^46+42x^47+39x^48+6x^49+12x^50+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 1.11 in 20.7 seconds.