The generator matrix

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

generates a code of length 48 over Z2[X]/(X^4) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+153x^44+532x^45+624x^46+626x^47+494x^48+504x^49+542x^50+276x^51+179x^52+68x^53+48x^54+42x^55+5x^56+2x^66

The gray image is a linear code over GF(2) with n=384, k=12 and d=176.
This code was found by Heurico 1.16 in 0.219 seconds.