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

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+205x^44+48x^45+280x^46+208x^47+621x^48+208x^49+244x^50+48x^51+119x^52+48x^54+13x^56+4x^58+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 0.188 seconds.