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 1 1 X X 1 1 X 1 X 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 0 0 X 2X 2X 2X X 2X 2X 2X 0 0 2X 0 X 0 X 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 2X 0 0 2X 2X 0 0 X 0 X X 0 X X 2X X 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 X 0 2X 0 0 2X 2X 0 2X 2X 2X 0 2X 0 2X 0 2X 0 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 X X 2X X 0 2X X X 0 2X 2X 2X X 0 2X X 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 2X 0 X 0 2X 0 2X X 0 2X X 2X 2X X 0 2X 0 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 2X X X X X 0 2X 0 2X 2X 2X X 2X 2X X 2X 0 0 generates a code of length 54 over Z3[X]/(X^2) who´s minimum homogenous weight is 90. Homogenous weight enumerator: w(x)=1x^0+48x^90+144x^93+194x^96+310x^99+588x^102+1104x^105+1772x^108+1250x^111+574x^114+194x^117+130x^120+110x^123+66x^126+46x^129+16x^132+10x^135+2x^138+2x^144 The gray image is a linear code over GF(3) with n=162, k=8 and d=90. This code was found by Heurico 1.16 in 0.982 seconds.