The generator matrix

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

generates a code of length 84 over Z3[X]/(X^3) who´s minimum homogenous weight is 156.

Homogenous weight enumerator: w(x)=1x^0+88x^156+108x^157+306x^158+834x^159+1404x^160+1188x^161+2782x^162+2796x^163+2964x^164+4568x^165+4380x^166+4116x^167+5934x^168+6054x^169+4404x^170+5248x^171+4032x^172+2262x^173+2320x^174+1296x^175+600x^176+458x^177+240x^178+144x^179+178x^180+60x^181+30x^182+110x^183+30x^184+18x^185+46x^186+6x^187+6x^188+22x^189+6x^190+6x^192+4x^198

The gray image is a linear code over GF(3) with n=756, k=10 and d=468.
This code was found by Heurico 1.16 in 12.9 seconds.