The generator matrix

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

generates a code of length 28 over Z3[X]/(X^2) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+54x^48+198x^50+196x^51+234x^53+110x^54+540x^56+94x^57+342x^59+162x^60+144x^62+74x^63+30x^66+2x^69+4x^72+2x^75

The gray image is a linear code over GF(3) with n=84, k=7 and d=48.
This code was found by Heurico 1.16 in 0.0427 seconds.