The generator matrix

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

generates a code of length 38 over Z2[X]/(X^3) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+161x^28+4x^29+276x^30+76x^31+868x^32+304x^33+1292x^34+656x^35+2261x^36+984x^37+2488x^38+1032x^39+2394x^40+688x^41+1320x^42+272x^43+808x^44+68x^45+244x^46+12x^47+141x^48+12x^50+17x^52+4x^56+1x^60

The gray image is a linear code over GF(2) with n=152, k=14 and d=56.
This code was found by Heurico 1.16 in 9.11 seconds.