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

generates a code of length 88 over Z3[X]/(X^3) who´s minimum homogenous weight is 162.

Homogenous weight enumerator: w(x)=1x^0+136x^162+36x^163+96x^164+432x^165+258x^166+792x^167+1138x^168+1584x^169+2040x^170+2338x^171+3588x^172+3600x^173+3304x^174+7014x^175+5262x^176+4434x^177+6936x^178+4512x^179+2916x^180+3360x^181+2112x^182+1486x^183+450x^184+480x^185+328x^186+66x^187+36x^188+128x^189+36x^190+24x^191+44x^192+30x^195+12x^198+10x^201+10x^204+4x^207+12x^210+2x^219+2x^228

The gray image is a linear code over GF(3) with n=792, k=10 and d=486.
This code was found by Heurico 1.16 in 14.3 seconds.