The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  X  X  X  X  X  1  X  X  1  1
 0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  0  X  0  X  X  X  0  X  0  X  X  0
 0  0  X  0  0  0  0  0  0  0  0  0  X  0  0  X  X  X  X  X  X  X  0  X  X  X  0  0  X  X  0  X  X  0  0
 0  0  0  X  0  0  0  0  0  0  0  0  X  X  X  X  X  0  X  X  X  X  X  0  X  0  X  X  0  X  0  0  0  X  0
 0  0  0  0  X  0  0  0  0  0  0  X  0  X  X  0  X  X  X  0  X  0  0  X  X  X  X  0  0  X  X  X  X  0  0
 0  0  0  0  0  X  0  0  0  0  0  X  0  0  X  X  X  X  X  0  0  X  X  0  0  0  X  X  X  X  0  0  X  0  0
 0  0  0  0  0  0  X  0  0  0  X  0  0  0  X  X  0  0  X  0  X  0  X  0  X  0  X  0  X  X  0  X  X  X  0
 0  0  0  0  0  0  0  X  0  0  X  0  0  X  0  0  X  0  0  X  X  0  X  0  X  X  0  X  0  X  X  X  0  X  0
 0  0  0  0  0  0  0  0  X  0  X  X  X  X  0  0  0  0  X  0  X  X  0  X  0  X  0  X  0  0  0  X  0  0  0
 0  0  0  0  0  0  0  0  0  X  X  X  X  0  0  X  X  X  X  X  X  0  X  0  0  X  X  X  X  0  0  0  0  X  0

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+56x^24+36x^26+4x^27+100x^28+32x^29+68x^30+112x^31+144x^32+224x^33+115x^34+280x^35+109x^36+224x^37+125x^38+112x^39+70x^40+32x^41+114x^42+4x^43+30x^44+46x^46+1x^48+7x^50+1x^52+1x^54

The gray image is a linear code over GF(2) with n=70, k=11 and d=24.
This code was found by Heurico 1.16 in 0.325 seconds.