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 X 0 1 1 1 X 1 1 1 1 1 1 X^2+2 1 1 1 1 1 1 X 1 1 1 1 2 X X 1 0 1 1 0 1 1 1 1 X^2 1 1 0 0 X 0 X^2+X+2 X^2 X^2+X X^2+2 X 2 X^2+X 0 X^2+X X^2+2 X X^2+2 X+2 0 X^2+X+2 X^2+2 X 2 X^2+X+2 2 X^2+X+2 0 X X^2+2 X X^2 X+2 X^2+2 X^2+X+2 0 X^2+X+2 2 X^2+X X^2+X+2 0 X+2 X^2 2 X^2+X+2 2 X^2+X X^2+2 X^2+X 0 X 0 X X^2+X 0 2 X^2+2 X+2 2 X^2+2 X X^2+2 X^2+X+2 X 0 X^2 2 0 X^2+X+2 X^2+X+2 X^2+X X^2+2 X^2 X^2+2 X^2+X+2 X X+2 X^2+X+2 0 X X X^2+X X^2 0 2 X^2+2 2 X X^2 X 2 0 0 X^2+2 0 X^2 2 0 0 0 X^2 X^2+2 X^2+2 X^2+2 X^2+2 2 X^2+2 0 2 2 X^2 X^2+2 0 X^2+2 X^2 2 2 X^2+2 2 X^2 X^2 2 X^2+2 X^2 X^2+2 2 X^2 0 X^2 0 2 X^2 2 X^2 2 2 X^2 2 0 X^2+2 X^2 X^2 0 X^2+2 0 X^2+2 0 2 2 X^2 2 X^2 2 0 X^2 0 X^2+2 0 0 X^2 X^2 X^2+2 X^2+2 2 X^2+2 X^2+2 X^2+2 X^2+2 X^2 0 0 X^2 0 2 2 X^2 0 0 X^2 0 0 0 X^2+2 0 0 2 X^2 X^2 X^2+2 X^2 0 X^2+2 X^2+2 X^2 2 2 X^2+2 X^2+2 X^2+2 2 0 X^2+2 0 X^2+2 0 X^2 X^2+2 2 2 0 X^2 X^2 2 X^2+2 X^2 2 0 X^2+2 0 0 X^2 X^2 2 X^2+2 2 0 X^2 2 X^2+2 0 X^2+2 2 X^2 X^2 2 X^2 2 X^2+2 X^2+2 X^2+2 2 X^2 X^2+2 0 0 X^2 0 0 X^2 X^2+2 X^2 X^2 X^2 2 0 X^2 0 X^2+2 0 X^2+2 X^2+2 2 0 2 0 2 0 0 0 0 0 2 2 2 2 0 2 0 0 2 0 2 2 0 0 2 0 0 2 0 0 0 0 2 2 2 2 2 2 2 2 2 0 2 0 0 0 2 2 0 0 0 0 2 0 2 0 2 0 2 0 2 2 0 2 0 2 0 0 2 2 2 2 0 2 0 2 0 0 2 0 2 2 2 2 2 0 2 0 2 0 2 2 0 2 generates a code of length 88 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 82. Homogenous weight enumerator: w(x)=1x^0+206x^82+8x^83+352x^84+200x^85+478x^86+576x^87+617x^88+544x^89+459x^90+184x^91+186x^92+24x^93+147x^94+71x^96+13x^98+18x^100+7x^102+2x^104+2x^106+1x^152 The gray image is a code over GF(2) with n=704, k=12 and d=328. This code was found by Heurico 1.16 in 31.1 seconds.