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 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^2 1 1 X^2 0 X X^2+2 X^2+X 0 X^2+X X^2+2 X+2 0 X^2+X X+2 X^2+2 0 X^2+X X^2+2 X 0 X^2+X X+2 X^2+2 X^2+X 0 X X^2+2 0 X^2+X X+2 X^2+2 0 X^2+X X^2+2 X+2 X+2 0 X^2+2 X^2+X 2 X^2+X+2 X^2 X X+2 0 X^2+2 X^2+X 2 X^2+X+2 X^2 X 0 X^2+X 2 X^2+X+2 X^2+2 X+2 X^2 X+2 X+2 0 2 X+2 X^2+2 X^2 X^2+X X^2+X+2 X 2 2 X^2+X+2 X^2+X+2 X^2 X^2 X^2+X+2 X^2+X+2 2 2 X^2 X^2 X+2 X X+2 X X 0 0 2 X^2+X X^2+X+2 X^2+X+2 X^2+X+2 2 X^2+X 2 X^2+2 X^2+X 2 X^2+2 0 0 2 0 0 0 2 0 0 0 0 2 0 0 2 0 0 2 2 2 2 0 2 2 0 2 2 2 0 2 2 2 0 2 0 2 2 0 0 2 0 2 0 2 2 0 0 2 2 0 2 0 0 2 0 0 2 2 2 0 0 0 2 2 2 0 0 2 0 2 2 2 0 0 0 2 2 0 2 0 0 0 2 2 2 0 2 2 0 2 2 0 0 2 2 2 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 0 2 2 0 2 0 0 2 0 2 0 2 2 0 0 2 0 2 0 2 2 0 2 0 2 0 0 2 0 2 2 0 0 2 2 2 0 0 0 2 0 2 2 0 2 0 0 2 0 0 2 0 2 2 2 2 0 0 0 0 2 0 0 2 0 2 0 2 2 2 0 0 0 0 2 0 2 0 0 2 2 2 2 2 0 2 2 0 0 0 2 2 2 0 0 2 2 2 0 0 2 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 0 0 2 2 0 0 2 2 2 2 0 0 2 0 2 0 2 0 0 2 2 0 0 0 0 0 0 2 2 0 0 2 0 0 2 0 2 2 0 2 2 0 0 2 0 2 2 0 0 0 0 0 0 2 0 2 2 2 0 2 2 0 2 2 0 0 2 0 0 2 2 2 2 2 0 2 0 2 0 0 2 0 0 2 0 2 0 2 2 0 0 2 0 2 0 2 2 0 2 0 2 0 2 0 0 2 2 0 2 2 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 0 0 2 0 2 0 0 2 0 2 2 2 2 0 2 0 2 0 2 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+195x^92+272x^94+1147x^96+224x^98+188x^100+16x^102+4x^104+1x^188 The gray image is a code over GF(2) with n=768, k=11 and d=368. This code was found by Heurico 1.16 in 1.22 seconds.