The generator matrix

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

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+150x^45+600x^46+230x^47+196x^48+186x^49+512x^50+110x^51+8x^52+16x^53+24x^54+12x^55+1x^60+1x^64+1x^68

The gray image is a linear code over GF(2) with n=384, k=11 and d=180.
This code was found by Heurico 1.16 in 0.516 seconds.