The generator matrix

 1  0  0  0  1  1  1 X^2  1  1 X^2+X  1  1 X^2 X^3+X^2  1  1 X^3+X X^2+X X^3+X^2+X X^3+X^2  1 X^2  1 X^3+X^2+X  1  1  0  1 X^3+X^2+X  1 X^2+X X^3 X^3+X^2+X  1  1  1  0  1  1 X^3+X X^2+X  0 X^3+X^2  1 X^2+X  1
 0  1  0  0  0 X^3+1 X^3+1  1 X^3+X^2+X X^3+X X^3+X^2+X X+1 X^2+1  1  1  X X^3+X+1 X^2  1  1 X^3+X^2+X X^3+X^2+X+1  1 X+1  1 X^3+X^2+X  X X^3+X X+1 X^3+X^2  X  1  1  1 X^3+X^2+X+1 X^3 X^3+X^2+X+1  1 X^3+X+1 X^2+X+1  1  1  X X^2 X+1 X^2  0
 0  0  1  0  1  1 X^2 X^2+1  0 X^3+1  1 X^2+1  X X^2+X X^3+X^2+X+1 X^3+X+1 X^3+X^2+X+1  1 X^3+X^2+1 X^2  1 X^2 X^3+X^2  X X^3+X+1 X^2+1 X^2+X X^3+X^2 X^3+X+1  1 X^2+X X+1 X^3+X^2+1 X^2+X X^3+X+1 X^3+1 X^3+X X^3+X  X X^2+1  X  X  1 X^3+X^2+X X^2+1  1  0
 0  0  0  1  1 X^2 X^2+1  1 X^2+X+1 X^3+X X^2+1 X^2+1 X^2 X^2+X+1 X^3+X^2+X X^3+1 X^3+X X^3+X^2 X^2+1 X+1 X^3+X^2+1 X^3+1 X^2+X X^3+X^2 X^3+X  0 X^3+X^2  1 X+1 X^3+X X^3+1 X^3+1 X^3+X X+1 X^3+X^2 X^3 X^3+1 X^3+X^2+X X^2+X+1 X^3 X^2+X+1 X^3+X^2+X X^2+X  1 X^3+X X^2 X^2
 0  0  0  0 X^3+X^2  0 X^3+X^2  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0 X^2 X^3+X^2 X^2 X^2 X^3+X^2 X^3 X^2 X^2 X^3+X^2 X^2 X^3+X^2 X^2 X^3+X^2 X^3 X^2 X^3 X^2 X^3+X^2 X^3 X^3 X^3+X^2 X^3 X^3  0  0 X^2 X^3 X^3 X^3+X^2  0 X^2

generates a code of length 47 over Z2[X]/(X^4) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+64x^39+668x^40+2222x^41+5607x^42+10962x^43+19818x^44+29396x^45+39911x^46+43650x^47+40761x^48+30730x^49+19887x^50+10408x^51+5116x^52+1792x^53+747x^54+250x^55+66x^56+52x^57+22x^58+10x^59+2x^60+2x^62

The gray image is a linear code over GF(2) with n=376, k=18 and d=156.
This code was found by Heurico 1.16 in 352 seconds.