The generator matrix 1 0 0 1 1 1 0 1 1 2 1 2 1 2 1 X+2 X 1 1 X 1 1 X+2 1 X 1 2 1 X 1 2 X+2 0 1 1 1 X 1 1 1 1 X 1 X+2 1 1 1 2 0 0 1 X+2 X+2 1 1 X X+2 1 1 X+2 1 X+2 1 1 X+2 X+2 0 1 X 1 1 X+2 0 1 1 1 0 X+2 1 0 1 X 1 1 X+2 X+2 1 0 1 0 0 1 1 1 2 1 1 3 1 2 X X+3 1 X+2 X X+3 1 X+2 X+1 1 X+2 2 X 1 X+3 1 1 0 1 1 X+2 X X+1 0 2 X 3 X+2 X 1 1 X 0 3 1 X+2 1 X+3 1 1 X+2 X+3 1 1 X+1 X+2 X+2 X+1 1 X 0 1 1 1 3 X 3 0 1 1 2 X X X X 3 1 X 1 X X+3 1 2 1 0 0 1 X+1 X+3 0 X+1 X 1 3 X+2 X 3 1 0 2 1 3 X+1 X+3 X X+2 1 X+3 1 0 2 1 X+2 X+1 1 X+2 3 0 1 X+2 1 3 X+2 1 X 1 X X+1 3 X+2 0 X+2 1 X 1 2 0 2 0 X+3 0 X+3 X+1 1 X+3 X X+3 2 X+2 3 X+1 X+1 1 X X+1 3 2 0 X+3 2 1 1 X+2 X+1 X+2 X X+1 X X 1 1 0 0 0 2 0 0 0 2 2 2 0 0 0 2 2 2 2 0 2 2 0 2 0 2 0 2 2 0 2 2 0 0 2 2 0 2 2 2 2 0 0 2 0 0 0 0 2 0 0 0 2 0 0 0 0 2 2 2 2 2 0 0 2 2 2 0 2 2 0 2 0 2 0 0 0 2 2 0 0 0 0 2 0 2 2 0 0 0 0 0 0 2 0 2 0 2 2 2 2 0 0 2 2 2 2 0 0 2 0 0 2 2 2 2 0 0 2 0 2 0 0 2 2 0 2 2 2 0 0 0 0 0 2 0 0 2 2 2 2 0 0 2 2 0 0 2 0 0 2 0 2 2 2 0 0 2 2 0 2 0 2 2 2 2 0 0 2 0 2 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 0 0 2 2 2 0 2 0 2 2 0 0 2 2 0 0 0 2 0 0 2 0 2 2 0 0 0 2 0 2 0 0 2 2 0 0 2 0 2 0 0 2 0 2 2 2 2 2 0 0 0 2 2 0 2 2 0 0 0 0 generates a code of length 87 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 80. Homogenous weight enumerator: w(x)=1x^0+81x^80+220x^81+345x^82+398x^83+373x^84+366x^85+313x^86+306x^87+328x^88+258x^89+219x^90+200x^91+176x^92+136x^93+88x^94+102x^95+56x^96+38x^97+47x^98+14x^99+7x^100+6x^101+11x^102+4x^103+2x^104+1x^106 The gray image is a code over GF(2) with n=348, k=12 and d=160. This code was found by Heurico 1.16 in 1.32 seconds.