The generator matrix

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

generates a code of length 48 over Z2[X]/(X^4) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+136x^42+594x^43+1756x^44+2730x^45+3988x^46+4688x^47+5198x^48+4892x^49+3877x^50+2390x^51+1454x^52+606x^53+299x^54+80x^55+47x^56+12x^57+11x^58+8x^59+1x^62

The gray image is a linear code over GF(2) with n=384, k=15 and d=168.
This code was found by Heurico 1.16 in 8.52 seconds.