The generator matrix

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

generates a code of length 40 over Z2[X]/(X^3) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+28x^28+159x^30+406x^32+839x^34+1778x^36+3085x^38+3747x^40+3139x^42+1842x^44+817x^46+337x^48+133x^50+46x^52+19x^54+5x^56+1x^58+2x^60

The gray image is a linear code over GF(2) with n=160, k=14 and d=56.
This code was found by Heurico 1.16 in 9.36 seconds.