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

generates a code of length 52 over Z2[X]/(X^4) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+27x^46+98x^47+62x^48+40x^49+102x^50+654x^51+142x^52+592x^53+110x^54+98x^55+42x^56+8x^57+10x^58+42x^59+2x^60+5x^62+4x^63+5x^64+2x^70+1x^72+1x^88

The gray image is a linear code over GF(2) with n=416, k=11 and d=184.
This code was found by Heurico 1.16 in 0.203 seconds.