The generator matrix

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

generates a code of length 93 over Z3[X]/(X^2) who´s minimum homogenous weight is 168.

Homogenous weight enumerator: w(x)=1x^0+168x^168+156x^169+198x^170+1058x^171+546x^172+732x^173+2204x^174+936x^175+1068x^176+3038x^177+1308x^178+1440x^179+3578x^180+1626x^181+1566x^182+4014x^183+1614x^184+1614x^185+4496x^186+1776x^187+1968x^188+4422x^189+1812x^190+1704x^191+3736x^192+1428x^193+1398x^194+2924x^195+984x^196+954x^197+1858x^198+594x^199+372x^200+812x^201+234x^202+72x^203+322x^204+96x^205+30x^206+108x^207+12x^208+28x^210+6x^212+10x^213+16x^216+6x^219+4x^222+2x^225

The gray image is a linear code over GF(3) with n=279, k=10 and d=168.
This code was found by Heurico 1.16 in 78.3 seconds.