The generator matrix

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

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+370x^45+850x^46+1294x^47+1306x^48+1200x^49+1042x^50+842x^51+510x^52+402x^53+242x^54+82x^55+15x^56+28x^57+2x^58+6x^59

The gray image is a linear code over GF(2) with n=392, k=13 and d=180.
This code was found by Heurico 1.16 in 1.16 seconds.