The generator matrix

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

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+192x^44+990x^45+1502x^46+1932x^47+2663x^48+2472x^49+2170x^50+1928x^51+1246x^52+682x^53+354x^54+148x^55+48x^56+28x^57+6x^58+8x^59+10x^60+4x^61

The gray image is a linear code over GF(2) with n=392, k=14 and d=176.
This code was found by Heurico 1.16 in 3.97 seconds.