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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  X
 0 X^3+X^2  0 X^2  0  0 X^2 X^3+X^2  0 X^3 X^3+X^2 X^3+X^2  0 X^3 X^3+X^2 X^3+X^2  0 X^2 X^2 X^3 X^3 X^3+X^2  0 X^2 X^2  0 X^3+X^2  0 X^3 X^3 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^2  0 X^2 X^3 X^2 X^3+X^2 X^3+X^2 X^3 X^3  0  0 X^3 X^2 X^3+X^2 X^3+X^2
 0  0 X^3+X^2 X^2  0 X^3+X^2 X^2  0  0 X^2 X^2 X^3  0 X^2 X^2 X^3 X^3 X^2 X^3 X^3+X^2 X^3 X^3 X^2 X^3+X^2 X^3 X^3 X^2 X^2 X^3+X^2 X^3 X^3+X^2  0 X^3  0  0 X^3 X^2 X^3 X^3+X^2 X^3+X^2 X^2  0 X^2 X^3+X^2 X^2 X^2 X^3+X^2  0  0
 0  0  0 X^3  0  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3  0 X^3  0 X^3  0 X^3  0  0  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3 X^3  0
 0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0 X^3 X^3  0 X^3 X^3  0  0 X^3  0 X^3 X^3 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+30x^45+38x^46+48x^47+90x^48+616x^49+96x^50+44x^51+19x^52+26x^53+10x^54+4x^55+1x^56+1x^92

The gray image is a linear code over GF(2) with n=392, k=10 and d=180.
This code was found by Heurico 1.16 in 0.11 seconds.