The generator matrix

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

generates a code of length 35 over Z2[X]/(X^2) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+60x^22+152x^24+210x^26+324x^28+642x^30+1141x^32+1533x^34+1558x^36+1186x^38+674x^40+345x^42+192x^44+94x^46+46x^48+23x^50+6x^52+2x^54+2x^56+1x^58

The gray image is a linear code over GF(2) with n=70, k=13 and d=22.
This code was found by Heurico 1.16 in 8.86 seconds.