The generator matrix
1 0 1 1 1 1 1 0 1 1 1 X 1 1 1 X 1 1 1 1 1 1 0 X X X 1 1 X 0
0 1 1 2 2X+1 0 2 1 X 2X+1 X+2 1 X X+1 X+2 1 X+1 0 X 1 2 X+2 1 1 X X 2X 2X 2X 1
0 0 2X 0 X X 2X 2X 2X 0 X X X 2X 2X 2X X 2X 0 0 X 0 X 0 2X X 0 X 0 0
generates a code of length 30 over Z3[X]/(X^2) who´s minimum homogenous weight is 57.
Homogenous weight enumerator: w(x)=1x^0+72x^57+18x^58+24x^59+24x^60+30x^61+24x^62+26x^63+6x^65+6x^66+6x^69+6x^70
The gray image is a linear code over GF(3) with n=90, k=5 and d=57.
This code was found by Heurico 1.16 in 0.00348 seconds.