The generator matrix

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

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+568x^46+592x^47+875x^48+592x^49+560x^50+256x^51+267x^52+144x^53+168x^54+16x^55+46x^56+8x^58+3x^60

The gray image is a linear code over GF(2) with n=392, k=12 and d=184.
This code was found by Heurico 1.16 in 5.5 seconds.