The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  1  0  1  X  1  0  1  X  1  1  0  1  X  1  1  0  X  1  X  X  1  X  X  1
 0  X  0 X^2+X  0 X^2+X  0 X^2+X  0 X^2+X  X X^2  X X^2+X X^2+X  0  X X^2+X X^2+X  0 X^2+X  X X^2+X X^2+X  0 X^2+X  X X^2+X  0 X^2+X X^2+X X^2+X  0  0  0
 0  0 X^2  0  0  0  0  0  0  0  0 X^2  0  0  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2
 0  0  0 X^2  0  0  0  0  0  0  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0 X^2  0  0 X^2  0  0  0
 0  0  0  0 X^2  0  0  0  0  0  0 X^2  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2  0 X^2 X^2  0 X^2
 0  0  0  0  0 X^2  0  0  0  0  0  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0 X^2  0
 0  0  0  0  0  0 X^2  0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0  0
 0  0  0  0  0  0  0 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0
 0  0  0  0  0  0  0  0 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2
 0  0  0  0  0  0  0  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0  0  0  0  0  0 X^2  0 X^2 X^2
 0  0  0  0  0  0  0  0  0  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0

generates a code of length 35 over Z2[X]/(X^3) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+131x^24+64x^26+586x^28+748x^30+256x^31+2057x^32+1024x^33+2416x^34+1536x^35+2902x^36+1024x^37+1640x^38+256x^39+1193x^40+240x^42+254x^44+12x^46+41x^48+2x^52+1x^64

The gray image is a linear code over GF(2) with n=140, k=14 and d=48.
This code was found by Heurico 1.16 in 7.73 seconds.