The generator matrix

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

generates a code of length 49 over Z2[X]/(X^4) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+124x^44+104x^45+467x^46+378x^47+697x^48+586x^49+702x^50+380x^51+443x^52+72x^53+105x^54+10x^55+12x^56+2x^57+2x^58+4x^61+3x^62+2x^64+1x^68+1x^70

The gray image is a linear code over GF(2) with n=392, k=12 and d=176.
This code was found by Heurico 1.16 in 0.234 seconds.