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

generates a code of length 55 over Z3[X]/(X^2) who´s minimum homogenous weight is 99.

Homogenous weight enumerator: w(x)=1x^0+62x^99+30x^101+236x^102+120x^104+300x^107+98x^108+510x^110+128x^111+366x^113+132x^116+42x^117+76x^120+34x^126+34x^129+6x^135+10x^138+2x^147

The gray image is a linear code over GF(3) with n=165, k=7 and d=99.
This code was found by Heurico 1.16 in 1.18 seconds.