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

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+24x^45+31x^46+36x^47+226x^48+404x^49+226x^50+20x^51+20x^52+20x^53+7x^54+8x^55+1x^96

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 0.078 seconds.