The generator matrix

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

generates a code of length 57 over Z3[X]/(X^3) who´s minimum homogenous weight is 102.

Homogenous weight enumerator: w(x)=1x^0+122x^102+108x^103+120x^104+356x^105+768x^106+972x^107+658x^108+3366x^109+3174x^110+1534x^111+9102x^112+5736x^113+2546x^114+11670x^115+6300x^116+1918x^117+6294x^118+2490x^119+500x^120+726x^121+138x^122+242x^123+36x^124+18x^125+58x^126+6x^127+6x^128+24x^129+18x^132+16x^135+16x^138+6x^141+2x^144+2x^153

The gray image is a linear code over GF(3) with n=513, k=10 and d=306.
This code was found by Heurico 1.16 in 8.89 seconds.