The generator matrix

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

generates a code of length 48 over Z2[X]/(X^3) who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+48x^41+120x^42+208x^43+270x^44+332x^45+416x^46+438x^47+497x^48+454x^49+387x^50+330x^51+226x^52+178x^53+82x^54+42x^55+20x^56+10x^57+12x^58+6x^59+8x^60+2x^61+6x^62+2x^64+1x^66

The gray image is a linear code over GF(2) with n=192, k=12 and d=82.
This code was found by Heurico 1.16 in 1.38 seconds.