The generator matrix

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

generates a code of length 39 over Z2[X]/(X^3) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+161x^28+96x^30+615x^32+64x^33+560x^34+640x^35+1343x^36+1984x^37+1184x^38+2816x^39+1653x^40+1984x^41+960x^42+640x^43+975x^44+64x^45+256x^46+316x^48+16x^50+49x^52+6x^56+1x^72

The gray image is a linear code over GF(2) with n=156, k=14 and d=56.
This code was found by Heurico 1.16 in 10.1 seconds.