The generator matrix

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

generates a code of length 89 over Z3[X]/(X^3) who´s minimum homogenous weight is 165.

Homogenous weight enumerator: w(x)=1x^0+236x^165+126x^167+876x^168+288x^169+1224x^170+2204x^171+900x^172+3204x^173+3848x^174+1710x^175+6516x^176+5508x^177+2538x^178+8262x^179+5964x^180+2340x^181+5544x^182+3632x^183+882x^184+1296x^185+1078x^186+90x^187+72x^188+438x^189+180x^192+14x^195+32x^198+16x^201+2x^204+10x^207+6x^210+6x^213+2x^222+2x^228+2x^231

The gray image is a linear code over GF(3) with n=801, k=10 and d=495.
This code was found by Heurico 1.16 in 16.3 seconds.