The generator matrix

 1  0  1  1  1 X^2+X  1  1  0  1  1 X^2+X  1  1  0 X^2+X  1  1  1  0 X^2+X  1  1  1  1  1  0  1 X^2+X  1  1  1  1  0  0  1  1  1
 0  1 X+1 X^2+X  1  1  0 X+1  1 X^2+X X^2+1  1  0 X+1  1  1 X^2+X  0 X^2+X  1  1 X^2+1 X+1 X^2+1  0 X^2+X  1 X+1  1 X^2+1 X+1  0 X^2+X  1  1 X+1  0  0
 0  0 X^2  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0  0  0  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0
 0  0  0 X^2  0  0  0  0  0  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 X^2  0 X^2  0 X^2  0 X^2  0  0 X^2
 0  0  0  0 X^2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0
 0  0  0  0  0 X^2  0  0  0  0  0 X^2  0  0 X^2 X^2  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 X^2  0 X^2  0  0
 0  0  0  0  0  0 X^2  0  0  0  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0  0 X^2  0  0 X^2  0 X^2  0 X^2 X^2
 0  0  0  0  0  0  0 X^2  0  0 X^2  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2 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  0  0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0  0  0  0 X^2
 0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2  0  0  0  0  0  0 X^2  0 X^2  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+112x^28+36x^30+32x^31+533x^32+352x^33+688x^34+1312x^35+1919x^36+2400x^37+1624x^38+2400x^39+1923x^40+1312x^41+688x^42+352x^43+515x^44+32x^45+36x^46+101x^48+13x^52+1x^56+1x^60+1x^64

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 6.41 seconds.