The generator matrix

 1  0  0  0  0  1  1  1  0  1  1  1  1  0  1  X  1  0  0  1  X  1  X  0  X  1  1  0  0  1  1  1  1  1  1
 0  1  0  0  0  0  0  0  0 X+1  1  1 X+1  1  X  1  X  1  1 X+1  1  X  1  X  X X+1  1  1  0 X+1 X+1 X+1  X  0  0
 0  0  1  0  0  0  1  1  1  1  1 X+1  0 X+1  X  X  0  0  1  0  1  1  0  1  X X+1 X+1 X+1  1  0  0  0  X  0  0
 0  0  0  1  0  1  1  0  1  0  X  1  1 X+1  0 X+1 X+1  1 X+1  X  0  0  0  X  1  1  0  X  1  X  1 X+1  X  0  0
 0  0  0  0  1  1  0  1  1 X+1  X  0 X+1  1 X+1  1  0  0  0  0  X  0  1  1 X+1  1  1 X+1  X X+1  0  1 X+1  X  0
 0  0  0  0  0  X  0  0  0  X  0  X  0  0  0  X  X  X  0  X  0  0  X  X  X  0  0  0  0  X  0  X  0  X  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  X  X  X  X  0  0  X  X  0  X  0
 0  0  0  0  0  0  0  X  0  0  X  0  0  X  X  0  X  0  X  X  0  0  X  0  X  X  0  X  X  X  X  X  X  X  0
 0  0  0  0  0  0  0  0  X  0  X  X  X  0  X  X  X  0  0  0  0  X  X  0  0  X  0  0  0  0  0  X  X  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+82x^24+433x^26+908x^28+1565x^30+2193x^32+2872x^34+3042x^36+2436x^38+1626x^40+753x^42+304x^44+125x^46+34x^48+6x^50+2x^52+2x^54

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 26 seconds.