The generator matrix

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

generates a code of length 47 over Z2[X]/(X^4) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+9x^46+22x^47+17x^48+8x^49+5x^50+2x^51

The gray image is a linear code over GF(2) with n=376, k=6 and d=184.
This code was found by Heurico 1.16 in 0.063 seconds.