The generator matrix

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

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+308x^40+608x^41+975x^42+1234x^43+1929x^44+2568x^45+3167x^46+3610x^47+3682x^48+3650x^49+3199x^50+2618x^51+1847x^52+1310x^53+908x^54+490x^55+277x^56+110x^57+70x^58+36x^59+20x^60+10x^61+1x^70

The gray image is a linear code over GF(2) with n=192, k=15 and d=78.
This code was found by Heurico 1.16 in 35.3 seconds.