The generator matrix

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

generates a code of length 40 over Z2[X]/(X^3) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+42x^26+128x^28+190x^30+260x^32+437x^34+836x^36+1378x^38+9806x^40+1379x^42+876x^44+468x^46+290x^48+147x^50+76x^52+42x^54+10x^56+11x^58+4x^60+2x^62+1x^64

The gray image is a linear code over GF(2) with n=160, k=14 and d=52.
This code was found by Heurico 1.16 in 10.6 seconds.