The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1  X  X  X  1  0  1  1  X  0  1  0  1  1  X  X  X  1  X  0  1  0  1  1
 0  1  0  0  0  1  1  1  0  0 X+1 X+1  1  0  1  X  0 X+1  0  0  1 X+1  0  1 X+1  1  1  1  1  1  X  X  0  1  0
 0  0  1  0  1  1  0  1  0  1  1  0  0  1  1  1  1 X+1 X+1  1  1  X  1 X+1  0  0  X  0 X+1  0  0  X  1  X  0
 0  0  0  1  1  0  1  1  1  0  1  0  1  1  0  0  X X+1 X+1 X+1  X X+1 X+1  0  X  1  X X+1 X+1  0  1  1  0 X+1  0
 0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  0  X  X  0  0  X  0  0
 0  0  0  0  0  X  0  0  0  0  0  X  0  X  X  0  X  X  0  X  0  X  X  X  X  0  X  X  0  0  0  X  0  0  0
 0  0  0  0  0  0  X  0  0  0  X  X  0  X  X  0  X  0  X  0  X  X  0  0  0  0  X  X  0  0  X  X  X  0  0
 0  0  0  0  0  0  0  X  0  0  X  0  X  0  X  0  X  X  X  X  0  0  0  0  X  0  X  0  X  0  0  X  0  X  X
 0  0  0  0  0  0  0  0  X  0  X  X  X  X  0  X  X  X  X  X  X  0  X  X  0  0  0  X  0  X  0  0  X  0  X
 0  0  0  0  0  0  0  0  0  X  0  0  0  0  X  X  0  X  X  X  X  0  0  X  0  X  X  X  0  0  X  X  X  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+57x^24+72x^25+231x^26+250x^27+421x^28+562x^29+771x^30+1010x^31+1176x^32+1386x^33+1348x^34+1588x^35+1487x^36+1476x^37+1302x^38+1012x^39+759x^40+524x^41+383x^42+210x^43+171x^44+74x^45+55x^46+26x^47+23x^48+2x^49+6x^50+1x^52

The gray image is a linear code over GF(2) with n=70, k=14 and d=24.
This code was found by Heurico 1.16 in 25.2 seconds.