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

generates a code of length 39 over Z2[X]/(X^3) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+45x^32+8x^33+49x^34+32x^35+18x^36+56x^37+268x^38+64x^39+288x^40+56x^41+38x^42+32x^43+12x^44+8x^45+17x^46+18x^48+9x^50+2x^52+2x^54+1x^62

The gray image is a linear code over GF(2) with n=156, k=10 and d=64.
This code was found by Heurico 1.16 in 0.0717 seconds.