The generator matrix

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

generates a code of length 48 over Z2[X]/(X^3) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+140x^39+622x^40+1186x^41+2003x^42+2710x^43+4034x^44+4914x^45+6475x^46+6780x^47+7435x^48+6988x^49+6625x^50+5222x^51+4209x^52+2682x^53+1687x^54+836x^55+578x^56+222x^57+100x^58+56x^59+16x^60+8x^61+6x^62+1x^68

The gray image is a linear code over GF(2) with n=192, k=16 and d=78.
This code was found by Heurico 1.13 in 35.1 seconds.