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

generates a code of length 51 over Z3[X]/(X^2) who´s minimum homogenous weight is 90.

Homogenous weight enumerator: w(x)=1x^0+52x^90+114x^93+180x^96+430x^99+708x^102+488x^105+60x^108+36x^111+34x^114+34x^117+24x^120+16x^123+6x^126+2x^132+2x^144

The gray image is a linear code over GF(3) with n=153, k=7 and d=90.
This code was found by Heurico 1.16 in 0.154 seconds.