The generator matrix

 1  0  0  1  1  1  X  1  1  0  1 X^3  X  1  1  1  1 X^3+X^2  1 X^2+X  1 X^3+X^2 X^3 X^3+X  1  1 X^2  1  1  1  1  1  1 X^3+X^2+X X^2+X X^2+X X^3+X  X  1  0 X^3+X^2+X X^2+X  X  1  0 X^3+X  1  1  X X^2 X^3  1
 0  1  0  0 X^2+1 X^3+X+1  1 X^3+X^2+X+1 X^2+X X^2 X^3+X+1  1  1 X^2 X^3+X^2+X  1 X^3+X^2+1 X^3+X^2+X  X  1 X^3+X^2+X  1  1 X^3+X X^3+X^2+X+1 X^2  1  0 X^3+X^2+X X^3+X^2+X+1 X^3+X^2+1 X^3+X^2+X+1 X^2+1  1  1 X^3+X  1 X^2+X X^2+X X^2 X^3  1  1  0  1  1 X^3 X^3 X^3  1  1  0
 0  0  1  1  1 X^2 X^2+1 X^3+X+1 X^3+1  1 X^3+X X^3+X^2 X^3+1 X^3+X^2+X X^3+1 X^3+X^2 X^2+X+1  1  0 X^3+X+1 X^3+X X^3+X X^2+1  1  X X^3+X^2+X X^3 X^2+1 X^3+X^2+X+1 X^2+X+1  1  1 X^3+X  0 X^3+1  1 X^3+X  1 X^2  1  1 X^3 X^2 X^3+X^2+X X^2+X+1 X+1  X X+1 X^3+X^2+X X+1 X^2+X X^2+X
 0  0  0  X X^3+X X^3 X^3+X X^3+X^2+X  X  X X^2 X^3+X X^2 X^2+X X^3+X^2 X^3+X^2+X X^3+X^2 X^3+X^2+X X^3+X  X  0 X^3+X X^2+X X^3 X^3+X  0 X^3+X^2 X^2 X^2+X X^3 X^2 X^2+X  X X^3+X^2+X  0 X^3+X^2  0 X^2+X  0  0  X X^2 X^3+X X^3+X^2+X X^2+X X^3 X^3+X^2 X^2 X^3+X X^2 X^3+X^2 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+194x^46+836x^47+1762x^48+2840x^49+3934x^50+4634x^51+4927x^52+4454x^53+3606x^54+2758x^55+1519x^56+752x^57+354x^58+88x^59+77x^60+14x^61+8x^62+2x^63+2x^64+4x^65+2x^67

The gray image is a linear code over GF(2) with n=416, k=15 and d=184.
This code was found by Heurico 1.16 in 9.28 seconds.