The generator matrix

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

generates a code of length 28 over Z3[X]/(X^2) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+8x^54+54x^56+16x^57+2x^84

The gray image is a linear code over GF(3) with n=84, k=4 and d=54.
This code was found by Heurico 1.16 in 0.00219 seconds.