The generator matrix

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

generates a code of length 49 over Z2[X]/(X^4) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+80x^45+237x^46+212x^47+362x^48+312x^49+315x^50+228x^51+207x^52+52x^53+23x^54+8x^55+5x^56+4x^57+1x^60+1x^74

The gray image is a linear code over GF(2) with n=392, k=11 and d=180.
This code was found by Heurico 1.16 in 0.094 seconds.