The generator matrix

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

generates a code of length 48 over Z2[X]/(X^4) who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+130x^41+1176x^42+2970x^43+6065x^44+9976x^45+15163x^46+18882x^47+21796x^48+19540x^49+15785x^50+9808x^51+5591x^52+2602x^53+1095x^54+298x^55+131x^56+34x^57+11x^58+10x^59+2x^61+2x^62+4x^65

The gray image is a linear code over GF(2) with n=384, k=17 and d=164.
This code was found by Heurico 1.16 in 93 seconds.