The generator matrix

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

generates a code of length 40 over Z2[X]/(X^3) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+119x^30+395x^32+28x^33+832x^34+268x^35+1380x^36+700x^37+2093x^38+1036x^39+2562x^40+1076x^41+2234x^42+708x^43+1430x^44+244x^45+737x^46+36x^47+346x^48+118x^50+30x^52+10x^54+1x^70

The gray image is a linear code over GF(2) with n=160, k=14 and d=60.
This code was found by Heurico 1.16 in 9.93 seconds.