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

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+16x^44+52x^45+27x^46+280x^47+295x^48+248x^49+32x^50+56x^51+8x^52+4x^53+4x^54+1x^94

The gray image is a linear code over GF(2) with n=384, k=10 and d=176.
This code was found by Heurico 1.16 in 0.094 seconds.