The generator matrix

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

generates a code of length 48 over Z2[X]/(X^4) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+512x^45+768x^46+634x^47+714x^48+544x^49+338x^50+210x^51+139x^52+132x^53+53x^54+48x^55+1x^58+2x^60

The gray image is a linear code over GF(2) with n=384, k=12 and d=180.
This code was found by Heurico 1.16 in 0.953 seconds.