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  0  1 X^2  1  1  1  X  0  1  1  1  1 X^3  1  1  1  X  X X^2  X  1  1  0 X^3+X^2  1  X  1
 0  X  0  X  0 X^3 X^2+X  X X^2 X^2+X X^2 X^3+X^2+X X^2 X^3+X^2 X^3+X X^3+X^2+X X^3+X X^2 X^3+X^2 X^2+X  0  X  X X^2 X^2  X X^3+X X^3+X^2 X^3+X^2  X X^3+X^2+X X^3+X^2 X^3+X^2 X^2  X  X  X X^3+X X^2+X X^3+X X^3+X^2 X^3+X X^2+X X^3+X  X  X X^3+X^2 X^3+X^2+X X^3+X^2
 0  0  X  X X^3+X^2 X^3+X^2+X X^2+X X^2 X^3+X^2 X^3  0 X^3+X^2  X X^2+X X^2+X  X X^3+X  X  0 X^3+X^2 X^3+X  0 X^3 X^2+X  X  X X^2+X X^3 X^3+X X^2+X  X X^3+X^2+X X^3+X^2 X^2+X X^3+X X^3+X^2 X^2+X X^3  0  0  X  0 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2+X  0 X^2 X^3
 0  0  0 X^3  0  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3  0  0 X^3 X^3 X^3  0  0 X^3 X^3  0  0  0  0  0 X^3 X^3 X^3 X^3  0 X^3  0  0  0 X^3 X^3  0 X^3  0 X^3 X^3 X^3
 0  0  0  0 X^3 X^3  0  0  0 X^3 X^3 X^3  0 X^3 X^3 X^3  0 X^3  0  0  0  0  0  0  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3  0  0  0  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+106x^44+226x^45+301x^46+612x^47+531x^48+760x^49+513x^50+450x^51+190x^52+178x^53+91x^54+56x^55+44x^56+20x^57+6x^58+2x^59+8x^60+1x^74

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 0.297 seconds.