The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1 X^2  1  X  X X^2  X  1  X  1  1
 0 X^3+X^2  0 X^2  0  0 X^2 X^2 X^3 X^3 X^2 X^3+X^2 X^3+X^2 X^3+X^2  0 X^3  0 X^2 X^3 X^2 X^3+X^2  0  0 X^2 X^2 X^2  0 X^3 X^3  0 X^2 X^3+X^2  0  0 X^3 X^3 X^3+X^2 X^3 X^3+X^2 X^3 X^2 X^2 X^2 X^2  0  0 X^3+X^2 X^3+X^2
 0  0 X^3+X^2 X^2  0 X^3+X^2 X^3+X^2  0 X^3 X^2 X^2  0 X^3 X^2 X^3 X^3+X^2  0 X^3+X^2 X^3+X^2 X^3  0 X^2  0 X^2 X^3 X^3  0  0 X^2 X^2 X^2 X^2  0 X^3  0 X^2  0 X^3  0 X^3+X^2 X^2 X^2 X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3 X^2
 0  0  0 X^3  0  0 X^3  0  0  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3  0  0 X^3  0 X^3 X^3  0 X^3  0  0  0  0  0  0  0 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3
 0  0  0  0 X^3  0  0  0  0 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0  0  0  0  0 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3  0 X^3
 0  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3  0 X^3 X^3 X^3  0  0  0 X^3 X^3  0  0  0  0 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3  0 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+20x^42+64x^43+67x^44+72x^45+179x^46+380x^47+516x^48+384x^49+160x^50+80x^51+43x^52+16x^53+21x^54+20x^55+11x^56+8x^57+3x^58+2x^60+1x^82

The gray image is a linear code over GF(2) with n=384, k=11 and d=168.
This code was found by Heurico 1.16 in 0.156 seconds.