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  1  1  1  X  1  1  1  1  1  1  1  1  1  0  1  1  1  1 X^3  X  1 X^3+X^2  X X^2  1 X^3+X^2  X
 0  X  0 X^2+X X^2 X^3+X^2+X X^3+X^2  X X^2+X X^3  0 X^3+X X^2 X^2+X X^2  X  0 X^2+X X^2 X^3+X X^3+X^2+X X^3+X^2 X^2+X X^3+X^2 X^3 X^3 X^3+X X^2  0 X^2+X  0 X^3+X X^3+X^2+X X^2+X X^3+X^2+X  X  0 X^3+X^2+X X^3+X^2 X^3+X  X X^2+X X^2  X X^2+X  X X^2  X X^2+X
 0  0 X^3+X^2  0 X^2 X^2  0 X^2  0 X^2 X^3 X^2 X^2 X^3+X^2  0 X^3  0 X^3 X^3+X^2 X^3+X^2 X^2 X^3  0 X^3+X^2  0 X^3+X^2 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^3 X^3+X^2 X^2 X^2 X^3  0 X^3 X^3 X^3 X^2 X^2 X^3 X^3 X^3 X^3 X^3+X^2 X^2 X^3  0
 0  0  0 X^3  0  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3  0  0  0  0  0  0  0 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3  0
 0  0  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3  0  0  0 X^3  0  0 X^3  0 X^3 X^3  0 X^3  0 X^3  0 X^3  0  0 X^3  0 X^3 X^3 X^3  0  0 X^3  0 X^3  0 X^3  0  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+156x^45+130x^46+264x^47+252x^48+508x^49+270x^50+196x^51+96x^52+100x^53+14x^54+48x^55+2x^56+4x^57+2x^58+4x^59+1x^80

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 117 seconds.