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 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X X X X X X X X X X X X^2 0 X X^2 X 0 X X 1 1 1 1 1 1 1 1 X X X X 0 X^2+2 0 X^2+2 0 X^2+2 0 X^2+2 0 X^2+2 0 X^2+2 0 X^2+2 0 X^2+2 0 X^2+2 0 X^2+2 0 X^2+2 0 X^2+2 0 X^2+2 0 X^2+2 0 X^2+2 0 X^2+2 2 X^2 2 X^2 2 X^2 2 X^2 2 X^2 2 X^2 2 X^2 2 X^2 2 X^2 2 X^2 2 X^2 2 X^2 2 X^2 2 X^2 2 X^2 2 X^2 X^2+2 X^2+2 X^2+2 X^2 X^2+2 X^2+2 X^2+2 X^2 X^2 X^2 X^2+2 X^2+2 X^2+2 X^2 0 X^2+2 0 X^2 0 2 0 0 0 0 2 2 2 2 2 0 0 0 0 0 2 0 0 0 2 0 0 0 0 0 2 0 2 0 0 2 0 2 0 2 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 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 0 2 0 0 2 2 0 2 2 2 0 0 0 2 2 2 2 0 0 2 0 0 0 0 0 2 0 0 0 2 0 0 0 0 0 2 0 2 2 2 2 2 2 2 2 2 2 0 2 0 2 0 2 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 2 2 2 2 0 2 0 2 0 0 0 0 2 2 0 0 2 2 0 2 2 0 0 0 0 0 2 0 2 0 0 2 2 2 2 2 0 2 2 0 2 0 0 2 0 2 0 2 0 2 2 0 2 0 0 0 0 0 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 0 0 0 0 0 0 2 2 2 0 0 0 2 2 2 0 0 0 2 2 0 2 2 2 0 2 2 2 0 2 2 2 2 0 0 0 0 0 0 0 0 2 0 2 2 2 2 0 2 0 2 2 0 0 2 2 2 2 0 0 0 0 2 2 2 2 0 0 0 0 2 2 2 2 0 0 0 0 2 2 2 2 0 0 0 0 2 2 2 2 0 0 0 0 2 2 2 2 0 0 0 2 2 0 0 0 0 2 2 0 2 2 2 0 0 2 2 0 2 2 0 2 0 0 2 0 0 2 0 0 0 0 generates a code of length 96 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 92. Homogenous weight enumerator: w(x)=1x^0+128x^92+160x^94+461x^96+160x^98+98x^100+6x^104+6x^108+3x^112+1x^144 The gray image is a code over GF(2) with n=768, k=10 and d=368. This code was found by Heurico 1.16 in 1.12 seconds.