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

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+576x^45+670x^46+728x^47+597x^48+522x^49+347x^50+352x^51+97x^52+114x^53+44x^54+44x^55+1x^56+2x^58+1x^62

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 7.3 seconds.