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

generates a code of length 51 over Z2[X]/(X^4) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+64x^46+54x^47+131x^48+30x^49+261x^50+988x^51+278x^52+28x^53+72x^54+46x^55+68x^56+6x^57+18x^58+2x^60+1x^98

The gray image is a linear code over GF(2) with n=408, k=11 and d=184.
This code was found by Heurico 1.16 in 0.156 seconds.