The generator matrix

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

generates a code of length 84 over Z3[X]/(X^3) who´s minimum homogenous weight is 157.

Homogenous weight enumerator: w(x)=1x^0+210x^157+300x^158+114x^159+420x^160+474x^161+206x^162+600x^163+1374x^164+778x^165+1500x^166+3540x^167+1400x^168+1806x^169+3468x^170+942x^171+588x^172+552x^173+86x^174+282x^175+198x^176+68x^177+174x^178+144x^179+24x^180+108x^181+72x^182+16x^183+114x^184+66x^185+2x^186+30x^187+18x^188+6x^189+2x^228

The gray image is a linear code over GF(3) with n=756, k=9 and d=471.
This code was found by Heurico 1.16 in 2.94 seconds.