The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  1  1 X^2  X  1  X  X  1  0  1 X^2  1
 0  X  0  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2+X  X  X X^2+X  X X^2+X X^2+X X^2+X X^2+X X^2  X X^2+X  X  X X^2 X^2  0 X^2+X X^2 X^2 X^2  X  0
 0  0  X  0  0  0  0  0  0  0  X X^2+X  X X^2+X X^2+X  X X^2+X  X  X X^2+X X^2  X  0 X^2 X^2  0 X^2  0  0  X X^2+X X^2+X  0 X^2 X^2 X^2+X X^2 X^2 X^2  0
 0  0  0  X  0  0  0  X X^2+X  X  X  X  0 X^2+X  X  0  0  0  X X^2 X^2+X X^2+X  X X^2  0 X^2  X  X X^2 X^2+X  0 X^2 X^2  0  X  0  0  X  X  0
 0  0  0  0  X  0  X  X  X X^2  0  0 X^2 X^2+X  X X^2+X  X  0 X^2+X X^2+X  X X^2 X^2+X  0 X^2  X X^2+X X^2 X^2 X^2 X^2 X^2  X X^2+X X^2 X^2  X X^2+X X^2  0
 0  0  0  0  0  X  X X^2 X^2+X X^2+X  0  X  X  X X^2  0  X  X X^2 X^2  0  X  X  X  0  0 X^2+X X^2  X X^2+X  0  X X^2+X  X X^2+X X^2+X  0  0 X^2  0
 0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2  0  0  0 X^2 X^2  0  0  0 X^2  0 X^2 X^2  0 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+78x^30+116x^31+203x^32+280x^33+429x^34+446x^35+660x^36+1094x^37+1489x^38+2140x^39+2418x^40+2132x^41+1570x^42+1168x^43+696x^44+496x^45+382x^46+208x^47+168x^48+84x^49+72x^50+18x^51+12x^52+10x^53+11x^54+2x^56+1x^66

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 10.3 seconds.