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

generates a code of length 58 over Z3[X]/(X^2) who´s minimum homogenous weight is 90.

Homogenous weight enumerator: w(x)=1x^0+92x^90+306x^93+544x^96+760x^99+1198x^102+1916x^105+3640x^108+6986x^111+11174x^114+12252x^117+9878x^120+5244x^123+2284x^126+1106x^129+748x^132+448x^135+262x^138+130x^141+40x^144+28x^147+8x^150+4x^153

The gray image is a linear code over GF(3) with n=174, k=10 and d=90.
This code was found by Heurico 1.16 in 81.7 seconds.