The generator matrix 1 0 1 1 1 X^2+X 1 1 X^2+2 1 X+2 1 1 1 0 1 1 X^2+X X^2+2 1 1 1 1 X+2 1 1 0 1 1 X^2+X 1 1 X^2+2 1 X+2 1 1 0 1 X^2+X 1 1 X^2+2 1 1 1 1 X+2 1 1 1 1 1 1 1 X 1 1 1 1 1 X 1 1 1 1 1 1 1 1 0 0 2 1 1 1 1 X^2+X X^2 2 1 1 1 1 X X X 0 1 X+1 X^2+X X^2+1 1 X^2+2 X^2+X+3 1 X+2 1 3 X+1 0 1 X^2+X X^2+1 1 1 X^2+2 X^2+X+3 X+2 3 1 0 X+1 1 X^2+X X^2+1 1 X^2+2 X^2+X+3 1 3 1 X+2 X^2+X 1 X+1 1 0 X^2+1 1 X^2+2 X^2+X+3 X+2 3 1 0 X^2+X+2 0 X 2 X^2 X^2+X 2 X^2+X+2 X^2 X^2+X+2 X^2 X^2+X 2 X^2+2 X^2+X X^2 X^2+X 2 0 X+1 X+1 1 1 1 X+2 X+3 X X+3 1 X 1 0 X^2+1 X^2+3 X^2+2 2 1 X^2+X 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 0 0 0 0 2 2 2 2 2 2 2 0 0 0 0 2 2 2 2 0 0 2 0 2 2 2 2 0 2 0 0 0 0 2 0 2 0 2 0 0 2 2 0 2 0 2 2 0 2 2 0 0 2 0 0 2 2 0 0 0 0 0 0 0 2 0 0 0 0 2 2 2 2 2 2 2 0 2 2 0 2 2 0 0 0 2 0 0 0 2 0 0 2 2 0 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 2 2 0 2 0 0 2 0 2 2 0 0 2 2 0 0 0 0 0 0 2 2 2 0 0 2 0 2 2 0 2 2 0 0 2 0 0 0 0 0 0 2 0 0 2 0 0 0 2 2 2 2 2 0 2 2 2 0 2 0 2 0 2 0 0 2 0 2 0 2 0 2 2 2 0 2 0 0 0 2 2 0 0 2 2 2 2 0 2 0 0 0 2 2 2 0 0 0 0 2 2 0 2 2 0 0 2 2 0 0 2 2 0 0 2 0 2 2 2 2 2 2 2 2 0 0 0 0 0 2 2 2 2 2 0 0 2 2 2 0 2 0 0 0 0 2 2 2 2 0 2 0 2 0 0 2 0 0 2 0 2 0 0 2 0 0 2 2 2 2 2 0 2 2 2 2 0 0 2 2 2 0 2 0 2 2 0 0 0 2 2 2 0 2 0 0 2 0 0 2 2 2 0 2 0 2 2 2 2 0 2 generates a code of length 87 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 82. Homogenous weight enumerator: w(x)=1x^0+252x^82+208x^83+616x^84+272x^85+478x^86+544x^87+458x^88+352x^89+425x^90+144x^91+248x^92+16x^93+58x^94+19x^96+2x^98+2x^120+1x^122 The gray image is a code over GF(2) with n=696, k=12 and d=328. This code was found by Heurico 1.16 in 15.7 seconds.