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.