The generator matrix

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

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+263x^46+966x^47+1487x^48+2118x^49+2281x^50+2678x^51+2196x^52+1834x^53+1114x^54+794x^55+365x^56+122x^57+85x^58+58x^59+14x^60+6x^61+1x^62+1x^64

The gray image is a linear code over GF(2) with n=408, k=14 and d=184.
This code was found by Heurico 1.16 in 2.73 seconds.