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

generates a code of length 47 over Z2[X]/(X^3) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+124x^38+4x^39+356x^40+56x^41+610x^42+224x^43+911x^44+456x^45+1106x^46+568x^47+1114x^48+456x^49+884x^50+224x^51+531x^52+56x^53+304x^54+4x^55+144x^56+42x^58+13x^60+2x^62+1x^64+1x^68

The gray image is a linear code over GF(2) with n=188, k=13 and d=76.
This code was found by Heurico 1.16 in 3.66 seconds.