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 X 1 0 1 1 1 1 1 X 1 0 1 1 2 1 1 1 1 1 1 X 1 0 1 1 1 X X 1 1 0 0 0 1 1 1 1 1 X 1 0 X 1 1 X 0 1 1 X X 1 X X 0 X 0 0 0 0 0 0 2 X X+2 X+2 X X X+2 X+2 2 2 0 X X X+2 X 0 X X 0 X+2 X 2 2 2 X+2 X+2 0 X+2 X+2 2 X X+2 X+2 X+2 0 2 X X 2 X+2 2 0 2 X 0 X+2 X+2 0 X+2 X+2 0 X X+2 2 X+2 X X+2 X X X 2 X+2 X 2 0 0 X+2 2 X X X+2 X X X X+2 X+2 0 X+2 X+2 0 X+2 0 0 X 0 0 0 X X+2 X+2 X X 2 X X 2 0 2 X+2 X+2 X+2 0 X X+2 X+2 0 X+2 X+2 2 2 0 0 2 2 X+2 0 X+2 X+2 2 X+2 2 X+2 X 2 0 X 0 X 0 X+2 2 X+2 0 X+2 X+2 X 0 X 0 0 2 0 2 2 X X 0 X+2 0 X 0 X 2 2 2 0 0 X 2 2 X+2 0 X 0 X+2 2 0 0 0 X 0 0 0 X 0 X X X 0 2 0 X X+2 X+2 X 2 2 0 0 0 2 2 X+2 X X+2 X X 0 X 2 X+2 X+2 X+2 X X+2 X+2 X+2 X X 0 2 X+2 0 X X+2 X X+2 0 0 X X+2 X+2 X X 2 X+2 X X 2 0 0 0 X X+2 X 2 2 X+2 0 X 0 X+2 X+2 2 X+2 0 2 X X X+2 2 X 2 X X+2 2 0 2 2 0 0 0 0 X X 2 X+2 X 2 X 0 X 0 X X X+2 X+2 0 2 X X 2 0 2 X+2 X+2 0 X 0 2 X X+2 X X+2 X+2 2 0 2 0 X 0 2 2 X 0 X+2 0 X+2 X X X 0 X+2 X 2 0 0 X X+2 X+2 X X+2 X+2 0 0 X+2 X+2 0 2 X 2 X+2 0 X+2 X+2 X+2 X+2 X+2 2 2 X 2 X+2 0 X+2 X+2 X X+2 0 0 0 0 0 2 2 2 0 0 0 2 0 0 0 2 2 2 2 2 0 2 2 0 0 2 0 2 2 2 2 0 0 0 2 2 2 0 0 0 2 0 0 2 2 2 2 2 0 0 0 2 2 0 0 2 0 0 2 2 0 0 0 0 2 0 0 2 2 2 0 0 2 0 0 2 2 2 2 0 0 2 2 2 0 2 2 0 0 generates a code of length 89 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 80. Homogenous weight enumerator: w(x)=1x^0+129x^80+8x^81+284x^82+44x^83+365x^84+132x^85+400x^86+244x^87+473x^88+224x^89+440x^90+168x^91+324x^92+132x^93+244x^94+52x^95+161x^96+16x^97+90x^98+4x^99+66x^100+40x^102+35x^104+6x^106+13x^108+1x^136 The gray image is a code over GF(2) with n=356, k=12 and d=160. This code was found by Heurico 1.16 in 2.21 seconds.