The generator matrix

 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  1  1  1  1  1  X  1  1  1 X^2  1  1  1  X  X  1  1  1  X X^2  1
 0 X^3+X^2  0  0  0 X^2 X^3+X^2 X^2  0 X^3 X^3+X^2 X^3+X^2  0 X^3 X^3+X^2 X^3+X^2  0 X^3 X^3+X^2 X^3+X^2 X^3 X^2 X^3+X^2 X^2 X^2 X^3  0  0  0 X^2 X^3+X^2 X^3 X^3+X^2 X^3 X^2 X^2 X^3 X^3 X^3  0 X^3+X^2  0 X^2 X^3  0 X^3+X^2 X^2  0 X^2  0 X^3
 0  0 X^3+X^2  0 X^2 X^2 X^2 X^3  0 X^3 X^2 X^3+X^2 X^2 X^2 X^3 X^3  0 X^3+X^2  0 X^3+X^2 X^3+X^2 X^2 X^3 X^3+X^2 X^3+X^2 X^2 X^3 X^3+X^2 X^3 X^3 X^2  0 X^2 X^2  0 X^2 X^3+X^2 X^3+X^2 X^3  0  0 X^3+X^2  0  0 X^2 X^3+X^2 X^2 X^3 X^2 X^3+X^2 X^3
 0  0  0 X^3+X^2 X^2 X^3 X^3+X^2 X^3+X^2  0 X^3+X^2 X^3 X^3+X^2 X^2  0 X^3+X^2  0 X^3 X^3+X^2 X^2 X^2  0  0 X^3 X^2 X^3 X^3 X^3+X^2 X^3+X^2 X^2 X^3 X^3+X^2 X^3 X^2 X^3 X^3 X^3+X^2  0 X^3+X^2 X^3 X^3+X^2  0 X^3 X^2 X^2 X^3+X^2 X^3+X^2 X^3 X^3 X^3 X^3  0
 0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3  0 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3 X^3  0  0  0 X^3  0  0  0 X^3 X^3 X^3  0  0  0  0  0 X^3 X^3  0  0 X^3 X^3  0  0 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+98x^46+4x^47+140x^48+128x^49+440x^50+504x^51+416x^52+128x^53+84x^54+4x^55+42x^56+40x^58+3x^60+10x^62+4x^64+1x^68+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 0.188 seconds.