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  1  1  1  1  1  1  1  X  1 X^2  1  1 X^2 X^2  X  1  1  X X^2
 0 X^3+X^2  0 X^2  0  0 X^2 X^2 X^3 X^3 X^2 X^3+X^2  0 X^2 X^3 X^2 X^3  0 X^2 X^3+X^2  0  0 X^2 X^2 X^3+X^2  0 X^3 X^3 X^3+X^2  0 X^2 X^2 X^3+X^2 X^3  0 X^2 X^2  0 X^3+X^2 X^2 X^2 X^2 X^3 X^3+X^2  0 X^3  0 X^2 X^3+X^2 X^2 X^2
 0  0 X^3+X^2 X^2  0 X^3+X^2 X^3+X^2  0 X^3 X^2 X^2  0 X^3 X^2 X^2  0 X^2  0 X^3+X^2 X^3  0 X^2 X^3 X^3+X^2 X^2  0  0 X^3+X^2 X^3 X^3+X^2 X^3 X^2 X^2 X^2 X^2 X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2  0 X^3+X^2 X^3  0 X^2 X^2
 0  0  0 X^3  0  0 X^3  0  0 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 X^3 X^3  0  0  0  0  0  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3 X^3  0
 0  0  0  0 X^3  0  0  0  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0  0  0  0  0  0 X^3  0  0  0 X^3 X^3  0 X^3 X^3 X^3  0
 0  0  0  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0  0 X^3  0 X^3 X^3 X^3  0  0  0  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0 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+130x^46+32x^47+94x^48+192x^49+324x^50+576x^51+256x^52+192x^53+120x^54+32x^55+31x^56+60x^58+6x^62+1x^64+1x^88

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 79 seconds.