The generator matrix

 1  0  0  1  1  1  0 X^3  1  1 X^2 X^3+X^2  1  1 X^3+X^2+X  1 X^3+X  1  1 X^2+X  1  1 X^3+X X^2+X  1  1  1  1  1  1  1  1  1  0  1  1  1 X^3+X  1  1  X X^3  1 X^3+X^2  X  0 X^3+X  1
 0  1  0  0 X^2+1 X^2+1  1 X^3+X^2+X X^3 X^3+X^2+1  1  1 X^2 X^3+1 X^3+X X^3+X^2+X  1 X^2+X+1  X  1 X^3+X+1 X^3+X^2+X  1 X^3+X^2 X^3+X+1 X^2+X+1 X^3+X^2+X X^3+X^2+X+1 X^3+X^2+1 X^3+X+1 X^3+X X^3+X^2  0  1  1  X X^3+X^2+1 X^3 X^2 X^3+X  1 X^3+X^2 X^3+X+1  1  1  X  1 X^3+X^2
 0  0  1 X+1 X^3+X+1 X^3 X^3+X^2+X+1  1 X^3+X^2+X X^2+1 X^3+X X^2+1 X^3+1 X^2+X  1 X^2+X+1 X^3+X^2+1 X^3+X^2  X X^2+X X^2+1  1 X^3+X^2+X+1  1 X^3+X+1  X  0 X^3+X^2 X^2+X  1 X^3+X X^3+X X^2+1 X^3+X^2+1 X^3+X^2+X+1 X^3+X^2+X+1 X^3+1  1  0 X+1 X^3+X  1 X^2+X  X X^2  1 X^2+X X^3+1
 0  0  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3  0  0 X^3 X^3  0 X^3 X^3  0  0  0  0  0  0  0 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0  0  0  0 X^3  0 X^3  0 X^3  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+353x^44+798x^45+1472x^46+1020x^47+1436x^48+964x^49+930x^50+480x^51+395x^52+174x^53+124x^54+20x^55+19x^56+2x^58+4x^60

The gray image is a linear code over GF(2) with n=384, k=13 and d=176.
This code was found by Heurico 1.16 in 1.13 seconds.