The generator matrix

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

generates a code of length 51 over Z2[X]/(X^4) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+144x^45+806x^46+1820x^47+2807x^48+3628x^49+4506x^50+5408x^51+4706x^52+4008x^53+2316x^54+1292x^55+838x^56+268x^57+98x^58+56x^59+44x^60+16x^61+2x^62+2x^64+2x^68

The gray image is a linear code over GF(2) with n=408, k=15 and d=180.
This code was found by Heurico 1.16 in 9.66 seconds.