The generator matrix
1 0 1 1 1 1 1 0 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 X 1 1
0 1 1 2 0 1 2 1 2X+1 1 0 2 2 X 1 2X+1 0 0 2X+1 2 X X+1 0 X X+2 1 X+2 0
0 0 2X 0 0 0 0 0 0 0 2X 2X 2X X 2X 2X 2X X X 0 X X X 2X X 2X 2X X
0 0 0 X 0 0 0 X 2X X 0 X 2X 0 X 0 X X X X X 2X 0 2X X X 0 2X
0 0 0 0 X 0 X X X X X 0 X 0 X X X 0 0 2X X 0 0 2X 2X X X X
0 0 0 0 0 2X 2X 0 2X X 0 2X X 0 2X X 0 2X X 0 0 2X X X X X 2X 2X
generates a code of length 28 over Z3[X]/(X^2) who´s minimum homogenous weight is 45.
Homogenous weight enumerator: w(x)=1x^0+70x^45+36x^47+298x^48+72x^49+90x^50+466x^51+252x^52+360x^53+812x^54+432x^55+450x^56+906x^57+522x^58+396x^59+670x^60+180x^61+126x^62+294x^63+72x^66+34x^69+20x^72+2x^75
The gray image is a linear code over GF(3) with n=84, k=8 and d=45.
This code was found by Heurico 1.16 in 0.278 seconds.