The generator matrix

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

generates a code of length 47 over Z2[X]/(X^3) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+340x^40+388x^41+1074x^42+824x^43+1598x^44+1260x^45+2132x^46+1244x^47+2158x^48+1204x^49+1590x^50+864x^51+953x^52+308x^53+308x^54+44x^55+60x^56+8x^57+12x^58+9x^60+4x^62+1x^72

The gray image is a linear code over GF(2) with n=188, k=14 and d=80.
This code was found by Heurico 1.13 in 3.33 seconds.