The generator matrix

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

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+81x^28+76x^29+218x^30+244x^31+411x^32+636x^33+883x^34+1160x^35+1518x^36+1968x^37+1896x^38+1952x^39+1617x^40+1216x^41+916x^42+664x^43+397x^44+196x^45+154x^46+76x^47+66x^48+4x^49+24x^50+4x^52+4x^54+1x^56+1x^66

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 9.21 seconds.