The generator matrix 1 0 0 0 0 1 1 1 1 1 1 2 1 X 2 2 X+2 1 X 1 1 1 0 1 1 1 X+2 1 X 2 X+2 1 2 1 1 2 1 X+2 2 1 1 X 1 2 1 1 2 1 1 2 1 2 1 2 X+2 2 1 1 1 X X+2 0 X 1 1 X 1 1 X+2 1 X 2 1 2 0 X 2 0 X+2 1 1 0 1 0 0 0 0 2 2 0 3 1 1 X+3 1 1 X X+2 X+2 1 1 X+3 X+1 1 X+1 X+2 3 X+2 X+2 X 1 1 0 1 2 3 1 2 2 1 2 3 1 1 2 3 1 X+2 3 X+2 X+2 X+2 X 3 1 0 1 2 1 X+2 1 1 1 1 X+1 2 1 0 1 1 X+1 1 2 X+2 1 X+2 1 1 1 1 X+1 X+2 0 0 1 0 0 0 3 X+1 1 1 X+3 X 2 3 3 1 1 X+1 X+1 0 X+2 1 3 X+1 0 X X 2 1 X+2 0 X 0 X+1 2 X+2 2 0 2 1 3 X+3 X+3 0 X+3 X 2 X+2 X+1 1 3 1 3 3 1 3 X+2 X+3 X 2 X+3 X 2 2 3 X 1 X+2 2 1 X+1 1 X 3 2 X X+3 1 1 0 0 0 0 0 1 0 1 1 X X X+2 X+3 1 3 0 X+1 1 X X+3 1 3 X+2 0 X X+1 1 0 1 X 1 1 X 3 2 1 X X+2 0 1 X+3 0 X X+2 X+3 X 3 3 1 X X+2 0 X 1 X+3 X+3 0 1 X X+2 X+1 2 X X+1 1 X+2 1 X+3 X 1 X+2 2 X+2 2 X X+3 X+2 X+3 X+2 2 X+3 X 2 0 0 0 0 1 1 2 0 X+1 2 X+3 X+3 1 X+3 X+1 X 3 1 X+2 X+2 X+1 X+3 X+2 X 0 2 X+1 X+1 3 X+2 X+1 X+1 X+3 0 0 0 1 X 1 X+3 X 3 X+3 1 0 3 X+3 0 X X X+1 3 X 2 X+3 X+1 X+2 3 X+3 X+3 X+2 X+2 0 1 X+3 3 1 X X X 3 3 2 1 1 1 0 X+2 2 X X 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 2 2 X+2 X X+2 X+2 X+2 X+2 X X X+2 X X+2 X+2 X X+2 X+2 X X X X+2 X X X X X X X X+2 X+2 2 2 X X+2 X+2 X 2 X 2 X+2 X X generates a code of length 81 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 69. Homogenous weight enumerator: w(x)=1x^0+142x^69+584x^70+1196x^71+1922x^72+2724x^73+3688x^74+5160x^75+6104x^76+7758x^77+9206x^78+9892x^79+10983x^80+11324x^81+11536x^82+10682x^83+9402x^84+7824x^85+6360x^86+4982x^87+3418x^88+2478x^89+1520x^90+962x^91+572x^92+308x^93+178x^94+74x^95+42x^96+18x^97+16x^98+12x^99+2x^100+2x^104 The gray image is a code over GF(2) with n=324, k=17 and d=138. This code was found by Heurico 1.13 in 287 seconds.