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 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 1 1 X 1 1
0 X 0 0 0 0 0 0 0 0 0 0 0 2X X X 2X 2X 2X 2X 0 X 2X 2X X 0 X X X X 0 X 0 X 2X X X 0 X 0 X X 2X X 0 X 2X 0 2X X 0 0
0 0 X 0 0 0 0 0 0 0 0 X X 0 0 X X 2X 0 2X 2X 2X X 2X X X X 2X 2X 2X X X X X 2X 0 0 0 0 2X 0 X X 0 X 2X 0 2X 0 X 0 0
0 0 0 X 0 0 0 0 X 2X 2X 2X X 0 0 0 X X 2X 0 2X X X X 0 X 2X 2X 0 2X 2X 2X X 2X 0 0 2X X 2X 0 0 0 X X 0 0 0 2X 0 2X 0 X
0 0 0 0 X 0 0 X 2X 0 2X 0 X 0 2X X 2X X X 0 0 0 X 2X X 0 X 2X 0 X 2X 2X 2X 2X 0 X 0 0 X X X X 0 0 2X 0 0 2X 2X 0 2X 0
0 0 0 0 0 X 0 2X 2X X 0 2X X 2X 0 2X 0 X 2X 2X 0 2X X X 0 2X 0 X 0 2X X 0 X 0 2X 2X X 2X X 0 2X X 0 0 X X 0 0 2X X X 0
0 0 0 0 0 0 X 2X 2X 2X 2X 2X 2X X 2X X 0 0 X 0 X X X X X X 2X 0 X X X X X 0 X X X 2X X X 2X 2X 0 X 2X X 2X 0 0 2X 0 X
generates a code of length 52 over Z3[X]/(X^2) who´s minimum homogenous weight is 87.
Homogenous weight enumerator: w(x)=1x^0+76x^87+172x^90+192x^93+256x^96+678x^99+1508x^102+1938x^105+1058x^108+194x^111+166x^114+140x^117+98x^120+46x^123+26x^126+6x^129+2x^132+2x^135+2x^144
The gray image is a linear code over GF(3) with n=156, k=8 and d=87.
This code was found by Heurico 1.16 in 0.979 seconds.