The generator matrix

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

generates a code of length 51 over Z2[X]/(X^4) who´s minimum homogenous weight is 47.

Homogenous weight enumerator: w(x)=1x^0+164x^47+509x^48+582x^49+687x^50+572x^51+498x^52+376x^53+349x^54+172x^55+111x^56+30x^57+18x^58+20x^59+4x^61+1x^62+1x^64+1x^66

The gray image is a linear code over GF(2) with n=408, k=12 and d=188.
This code was found by Heurico 1.16 in 0.234 seconds.