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 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 1 1 1 X 1 1 1 1 X 1 1 1 X 1 X 1 1 X 1 1 1 1 X 1 1 1 0 X 0 0 0 0 0 0 0 0 0 0 0 0 X 2X 2X X 2X 2X 2X X X 2X X 2X X 0 2X 2X 0 X 2X X X 0 0 2X 2X X 2X 2X X X X 2X 2X 2X 0 0 2X 0 2X 2X 2X 0 0 0 0 2X X X 0 2X 0 X X 0 0 X 0 2X 2X 0 X 0 0 X 0 0 X 0 0 0 0 0 0 0 0 X 2X 2X 2X 2X 0 X 0 X X 2X X 2X 0 2X 0 X 0 2X 0 2X X X X X 2X X 0 2X X 0 0 X X X 0 2X 2X X 2X 2X 0 X X 0 X X 2X 0 X X X X X X X 2X 0 0 X 0 0 X 2X X 2X X 0 0 0 X 0 0 0 0 X 2X 2X 2X 0 0 X 0 X 2X X 2X 2X 2X 2X 0 0 2X 2X 2X 2X 2X 0 0 0 X 2X 2X 2X 0 0 X 0 X X 2X 0 2X 2X 0 X X 2X 2X 2X X 2X X X 2X 2X 0 X 2X 0 2X 0 0 2X X X 2X 2X 2X 0 0 0 X 0 0 0 0 0 0 X 0 0 X 2X 0 2X 0 0 2X 2X X X X 2X X 0 2X X 2X X X X 2X 2X 2X X 0 0 0 2X 0 2X 2X 0 0 X 0 2X 2X 2X 2X X 2X X 2X 2X 2X 2X X X 2X 2X X X 0 0 X 2X 2X 2X X 2X 2X 2X 2X 2X 2X 2X 2X 2X X X 0 0 0 0 0 0 X 0 2X 2X X 0 2X 2X 2X 2X 2X 2X 0 X 0 0 2X 2X 0 X 0 0 X 2X X X 0 X 2X 0 X 2X 2X X 2X 0 0 2X X X 2X 0 X X 2X X X X 0 X 2X X X 0 X X 0 2X 0 X X 0 2X X 2X 0 X 2X 2X 2X 0 X X 0 0 0 0 0 0 X 2X 2X 2X 2X 2X 2X X X X 0 2X 0 0 X 0 2X 2X 2X 2X X 2X 2X X 0 0 0 0 0 2X X 2X 2X 0 2X 2X X 0 0 0 0 0 2X 0 2X 2X 0 2X 0 2X 2X 0 X X 2X 0 X X 0 X 0 X 0 2X X X X 2X 2X X 2X 0 generates a code of length 78 over Z3[X]/(X^2) who´s minimum homogenous weight is 138. Homogenous weight enumerator: w(x)=1x^0+90x^138+188x^141+202x^144+42x^145+230x^147+126x^148+218x^150+630x^151+172x^153+1050x^154+188x^156+1386x^157+154x^159+882x^160+144x^162+258x^163+150x^165+118x^168+108x^171+70x^174+52x^177+38x^180+28x^183+24x^186+8x^189+2x^198+2x^213 The gray image is a linear code over GF(3) with n=234, k=8 and d=138. This code was found by Heurico 1.16 in 1.64 seconds.