The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X X^2 X^2  X  1  0 X^2  0  0  X  1  1  1  X  X  1  X  1  X  0  1
 0  X  0  0  0  X X^2+X  X  0 X^2 X^2  X X^2+X  X  0  X X^2 X^2 X^2 X^2  X  X X^2+X  X  X  X  X X^2 X^2+X  0 X^2 X^2+X  0 X^2+X  X X^2 X^2 X^2+X  0  X
 0  0  X  0  X  X X^2+X  0  0  0  X X^2  X  X  X X^2  X  0  X X^2+X  X  0  0 X^2+X X^2+X X^2  X X^2 X^2  0  0 X^2 X^2+X  X  0  X  X  0  X  0
 0  0  0  X  X  0 X^2+X  X  0  X  0  X X^2+X X^2  X  0  0 X^2  0 X^2+X X^2  X X^2  0  X X^2+X  X  X X^2+X  0  X X^2+X X^2  X  0  X  X X^2  0 X^2+X
 0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0
 0  0  0  0  0 X^2  0  0  0 X^2 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 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0  0 X^2
 0  0  0  0  0  0 X^2  0  0  0 X^2  0  0  0  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2
 0  0  0  0  0  0  0 X^2  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0
 0  0  0  0  0  0  0  0 X^2  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2  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+71x^30+92x^31+198x^32+348x^33+460x^34+658x^35+941x^36+1188x^37+1488x^38+1784x^39+1836x^40+1784x^41+1600x^42+1284x^43+914x^44+696x^45+396x^46+252x^47+187x^48+76x^49+68x^50+26x^51+17x^52+4x^53+12x^54+2x^56+1x^62

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 10.1 seconds.