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

generates a code of length 91 over Z3[X]/(X^3) who´s minimum homogenous weight is 178.

Homogenous weight enumerator: w(x)=1x^0+132x^178+216x^179+182x^180+384x^181+384x^182+160x^183+456x^184+204x^185+60x^186+6x^188+2x^255

The gray image is a linear code over GF(3) with n=819, k=7 and d=534.
This code was found by Heurico 1.16 in 0.777 seconds.