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  X  1  1  1  1  X  1  1  1  1  1  X  1  1  1  1  1  X  1  1  1  X  X  1 X^2  X  1 X^2  1  1  1
 0 X^2  0  0  0  0  0  0  0  0 X^2 2X^2 2X^2 X^2 X^2 X^2  0 2X^2 X^2 2X^2 X^2  0 X^2  0 2X^2 X^2  0 2X^2 X^2 2X^2 2X^2 2X^2 X^2 X^2 X^2  0 2X^2 2X^2  0  0  0 X^2 2X^2 X^2  0 X^2 2X^2 2X^2 X^2 2X^2 2X^2 2X^2 X^2  0 2X^2 X^2 2X^2 2X^2 X^2 X^2 2X^2 X^2 2X^2  0 X^2 X^2 2X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 2X^2  0 2X^2  0 X^2  0 X^2  0 X^2 X^2
 0  0 X^2  0  0  0  0 X^2 2X^2 2X^2 2X^2  0  0 2X^2 X^2 2X^2 X^2  0 X^2 X^2  0 2X^2 2X^2  0 X^2 X^2 2X^2  0 X^2  0 2X^2 2X^2 2X^2 X^2 2X^2  0 2X^2 2X^2 X^2 2X^2 X^2 2X^2 2X^2 2X^2  0 2X^2  0 2X^2  0 X^2  0 2X^2  0 X^2  0  0 2X^2  0  0 2X^2  0 X^2 2X^2  0 2X^2 X^2 X^2 X^2 X^2 2X^2  0 X^2  0  0 2X^2 X^2  0 X^2 X^2 2X^2  0 2X^2 2X^2 2X^2
 0  0  0 X^2  0  0 X^2 2X^2  0 2X^2  0  0 2X^2 X^2 X^2 2X^2  0 X^2  0 2X^2  0 2X^2 2X^2  0 2X^2  0 X^2 2X^2 2X^2 X^2 X^2 X^2 2X^2  0  0 2X^2 2X^2 X^2 2X^2 X^2  0 2X^2 2X^2 X^2 X^2 X^2 2X^2 2X^2 2X^2  0 X^2 2X^2  0 X^2  0  0 X^2  0 X^2  0 X^2 2X^2 2X^2 X^2 2X^2 2X^2 X^2 2X^2  0 X^2 X^2 X^2 X^2 2X^2  0 X^2 X^2 X^2 X^2 X^2 2X^2 X^2 2X^2 X^2
 0  0  0  0 X^2  0 2X^2 2X^2 X^2  0 2X^2 2X^2 2X^2  0 2X^2 2X^2  0 2X^2 X^2  0 2X^2 2X^2  0 X^2 2X^2  0 2X^2 X^2  0 X^2  0 X^2  0 2X^2  0 2X^2  0 2X^2 X^2  0 2X^2 X^2 2X^2 X^2 2X^2 2X^2  0 2X^2  0 X^2 X^2  0 X^2 2X^2  0 X^2  0  0 2X^2 2X^2 2X^2 X^2 2X^2  0 X^2 X^2 2X^2 2X^2 2X^2 2X^2 X^2 2X^2  0 X^2 2X^2  0  0 X^2  0 2X^2 2X^2  0 X^2 2X^2
 0  0  0  0  0 X^2 2X^2 2X^2 2X^2 2X^2 2X^2 2X^2 X^2 2X^2 X^2 X^2 2X^2 X^2 2X^2 2X^2 2X^2 2X^2  0 2X^2  0 X^2  0  0 2X^2 X^2 2X^2  0 2X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2 2X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 2X^2 2X^2 X^2 2X^2 2X^2 2X^2 X^2 X^2 2X^2  0  0 2X^2 X^2 2X^2 X^2 X^2 X^2 X^2 2X^2 2X^2 X^2  0  0 2X^2 2X^2 2X^2 X^2  0  0 X^2 X^2 2X^2 2X^2 2X^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+106x^156+174x^159+290x^162+486x^164+330x^165+1944x^167+480x^168+1944x^170+390x^171+224x^174+60x^177+30x^180+18x^183+34x^186+8x^189+16x^192+6x^195+6x^198+8x^201+2x^207+2x^213+2x^225

The gray image is a linear code over GF(3) with n=756, k=8 and d=468.
This code was found by Heurico 1.16 in 16.1 seconds.