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

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+60x^102+112x^105+54x^107+142x^108+270x^110+70x^111+486x^113+4460x^114+432x^116+50x^117+216x^119+46x^120+44x^123+34x^126+26x^129+24x^132+14x^135+12x^138+2x^141+2x^144+2x^150+2x^156

The gray image is a linear code over GF(3) with n=513, k=8 and d=306.
This code was found by Heurico 1.16 in 0.371 seconds.