The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1 X^3+X^2  X  1  1  1  1  1  1 X^2 X^2  X  X
 0  X  0  X X^3  0 X^3+X  X X^2 X^2+X X^2 X^3+X^2+X X^3+X^2 X^2 X^2+X X^2+X  0 X^3 X^3+X  X X^2  X X^3+X^2+X  X X^2  0 X^2+X X^2  X X^3+X^2+X X^3+X^2 X^2+X  0 X^2+X X^3+X X^3+X^2+X X^3 X^3 X^3+X X^3+X^2+X  0 X^3+X^2 X^3+X X^3+X^2 X^2  X X^3 X^3+X^2
 0  0  X  X X^2 X^2+X X^2+X X^2 X^2 X^3  X X^3+X  0 X^2+X X^3+X^2+X X^3+X^2  0 X^3+X^2+X X^2+X  X X^2+X X^3+X  X X^3+X^2 X^3+X X^3+X X^3+X^2+X X^3  0  X X^2 X^2 X^2 X^3 X^3+X  0  X  X X^3 X^2+X  X  X  0 X^3  X  X X^3+X X^2+X
 0  0  0 X^3 X^3 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  0 X^3  0  0 X^3  0  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3  0 X^3 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+95x^44+192x^45+286x^46+280x^47+436x^48+264x^49+236x^50+112x^51+55x^52+40x^53+30x^54+8x^55+12x^56+1x^80

The gray image is a linear code over GF(2) with n=384, k=11 and d=176.
This code was found by Heurico 1.16 in 0.125 seconds.