The generator matrix

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

generates a code of length 49 over Z2[X]/(X^4) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+378x^46+192x^47+371x^48+128x^49+508x^50+192x^51+202x^52+70x^54+1x^60+4x^62+1x^76

The gray image is a linear code over GF(2) with n=392, k=11 and d=184.
This code was found by Heurico 1.16 in 22.9 seconds.