The generator matrix

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

generates a code of length 48 over Z2[X]/(X^4) who´s minimum homogenous weight is 43.

Homogenous weight enumerator: w(x)=1x^0+226x^43+871x^44+1566x^45+2178x^46+2178x^47+2468x^48+2450x^49+2086x^50+1152x^51+719x^52+258x^53+94x^54+84x^55+19x^56+14x^57+10x^58+6x^59+2x^60+2x^63

The gray image is a linear code over GF(2) with n=384, k=14 and d=172.
This code was found by Heurico 1.16 in 2.45 seconds.