The generator matrix

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

generates a code of length 31 over Z3[X]/(X^3) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+62x^51+168x^53+284x^54+1122x^56+1170x^57+2430x^58+4686x^59+4480x^60+9720x^61+9066x^62+6952x^63+9720x^64+6276x^65+2100x^66+498x^68+154x^69+54x^71+40x^72+36x^75+20x^78+4x^81+6x^84

The gray image is a linear code over GF(3) with n=279, k=10 and d=153.
This code was found by Heurico 1.16 in 3.95 seconds.