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

generates a code of length 58 over Z3[X]/(X^3) who´s minimum homogenous weight is 102.

Homogenous weight enumerator: w(x)=1x^0+34x^102+12x^103+30x^104+258x^105+234x^106+378x^107+480x^108+1116x^109+1926x^110+1376x^111+2958x^112+5934x^113+3102x^114+5766x^115+10062x^116+4052x^117+5874x^118+7794x^119+2394x^120+2640x^121+1488x^122+398x^123+318x^124+90x^125+166x^126+30x^127+66x^129+6x^130+16x^132+18x^135+14x^138+4x^141+8x^144+4x^147+2x^150

The gray image is a linear code over GF(3) with n=522, k=10 and d=306.
This code was found by Heurico 1.16 in 8.53 seconds.