The generator matrix

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

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+168x^48+210x^49+342x^50+478x^51+372x^52+414x^53+614x^54+498x^55+426x^56+544x^57+432x^58+474x^59+570x^60+294x^61+252x^62+264x^63+132x^64+24x^65+32x^66+6x^67+12x^68+2x^69

The gray image is a linear code over GF(3) with n=84, k=8 and d=48.
This code was found by Heurico 1.16 in 0.225 seconds.