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

generates a code of length 56 over Z3[X]/(X^2) who´s minimum homogenous weight is 90.

Homogenous weight enumerator: w(x)=1x^0+74x^90+242x^93+386x^96+514x^99+882x^102+1648x^105+2706x^108+3708x^111+3890x^114+2814x^117+1336x^120+666x^123+332x^126+224x^129+148x^132+64x^135+32x^138+12x^141+2x^147+2x^153

The gray image is a linear code over GF(3) with n=168, k=9 and d=90.
This code was found by Heurico 1.16 in 9.46 seconds.