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

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+36x^46+132x^47+198x^48+312x^49+203x^50+86x^51+33x^52+12x^53+8x^54+2x^55+1x^94

The gray image is a linear code over GF(2) with n=392, k=10 and d=184.
This code was found by Heurico 1.16 in 0.078 seconds.