The generator matrix

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

generates a code of length 28 over Z3[X]/(X^2) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+306x^44+316x^45+1614x^47+1242x^48+4086x^50+2340x^51+7716x^53+4504x^54+10572x^56+5640x^57+9354x^59+3978x^60+4614x^62+1398x^63+1044x^65+240x^66+60x^68+14x^72+6x^75+4x^81

The gray image is a linear code over GF(3) with n=84, k=10 and d=44.
This code was found by Heurico 1.16 in 37.7 seconds.