The generator matrix

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

generates a code of length 35 over Z2[X]/(X^3) who´s minimum homogenous weight is 25.

Homogenous weight enumerator: w(x)=1x^0+38x^25+76x^26+160x^27+288x^28+384x^29+531x^30+770x^31+1224x^32+1592x^33+1984x^34+2208x^35+1945x^36+1704x^37+1279x^38+836x^39+562x^40+334x^41+192x^42+112x^43+70x^44+40x^45+29x^46+10x^47+5x^48+4x^49+4x^50+1x^52+1x^54

The gray image is a linear code over GF(2) with n=140, k=14 and d=50.
This code was found by Heurico 1.16 in 8.79 seconds.