The generator matrix 1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 1 0 0 1 0 X 1 1 1 0 1 X 1 1 0 1 1 2 0 1 2 1 0 2X+1 2 1 0 2X+1 2 1 0 1 1 2X+1 1 1 2 0 X X 2X+1 1 0 0 0 0 2X 0 0 0 0 0 0 2X X 2X 2X X 0 X 0 0 2X 0 X 2X X X 0 0 2X X X 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 X X X X X X X 2X 0 0 X X X 0 2X X 0 0 0 0 X 0 0 0 0 0 0 0 0 2X 2X X 2X X 0 0 X X X X 2X 0 X X X X 0 0 0 0 0 2X 0 0 X 2X 2X X 2X 0 2X 0 2X 0 0 X X X 2X X 0 2X 2X 2X 0 0 0 0 0 0 0 0 X 0 X 0 X X X X X 2X 0 0 2X 2X X 0 2X X X 0 2X 2X 0 0 0 0 0 0 0 0 0 X X X X 0 2X 2X 0 0 X X X 2X X 0 X 2X 2X 2X 0 0 0 0 generates a code of length 30 over Z3[X]/(X^2) who´s minimum homogenous weight is 42. Homogenous weight enumerator: w(x)=1x^0+62x^42+212x^45+84x^46+426x^48+552x^49+730x^51+2010x^52+1788x^54+5178x^55+3690x^57+9318x^58+5256x^60+10992x^61+4334x^63+7698x^64+2042x^66+3090x^67+660x^69+444x^70+312x^72+98x^75+40x^78+22x^81+8x^84+2x^87 The gray image is a linear code over GF(3) with n=90, k=10 and d=42. This code was found by Heurico 1.16 in 16.3 seconds.