The generator matrix 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 X 1 1 1 X 2X 1 1 1 2X 0 1 1 1 1 1 0 1 X 1 1 1 1 1 2X X 1 1 X 1 2X X 1 1 1 2X 1 2X 1 1 1 2X 1 1 0 0 1 X 0 0 X 1 1 1 X 1 2X 1 1 1 1 X 2X 2X 1 1 1 1 0 1 0 0 2X 0 X X 2X 2X 2X 2X 2X+1 1 X+2 1 2X+1 X+2 2X+2 1 1 2X+1 X+1 2 1 1 1 2X+2 2X+2 X+1 2X+1 1 2X+2 1 X+2 1 0 0 X X 0 X+1 2 1 0 1 2X 1 2X+1 X+2 0 2 1 X+1 2 2 1 2 X+2 X 1 X+2 1 2X 1 1 0 2 2X+2 1 2X 1 0 2X 2X+2 2X 1 1 1 2X+2 2X+1 2X+1 X+2 0 0 1 0 0 X 2X+1 2 2X+1 2 X+1 X+2 2X+2 2 2X+2 X 2 X+2 X+2 2X X+2 2X 1 0 X+1 2X+1 X+1 0 2X 0 X X+1 2X+1 2X+2 2X+1 1 1 X+1 X+2 1 1 2 2X 2 2X+2 1 1 0 2X+1 X+1 0 X+2 X+2 2X+2 2X+1 X 2X+2 1 X 1 X 2X+2 2X 1 2X+1 2X+2 2 X+1 2X+2 1 2X+2 2X+1 2X X+2 2X+2 2X X+1 2 2X+1 2X+2 X+2 X+1 0 0 0 0 1 2X+1 2X+2 2X+1 1 2X+2 0 X 2 X+2 X+1 X+1 2X+2 2X X+2 0 X+1 1 X 2X+1 X+1 2 1 X+2 X 2X+2 2 X+1 2X X+2 X X 0 X 2 X 2 X+1 2X 2X+1 2 2 X+1 0 2 0 0 1 0 2X+2 X+1 2X+2 2 0 2X+2 2X X 2X+2 1 2X+1 X+2 2 2X 2X+1 X+1 2X 2X+2 0 2 2X 2X+1 X 2 1 1 X+1 X+1 2X X+2 2X+2 generates a code of length 83 over Z3[X]/(X^2) who´s minimum homogenous weight is 156. Homogenous weight enumerator: w(x)=1x^0+540x^156+1086x^159+1282x^162+984x^165+792x^168+616x^171+480x^174+330x^177+292x^180+78x^183+42x^186+32x^189+6x^192 The gray image is a linear code over GF(3) with n=249, k=8 and d=156. This code was found by Heurico 1.16 in 8.03 seconds.