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 X 1 1 1 1 1 1 1 1 1 2 1 X 1 1 1 1 1 1 0 1 1 X 1 1 1 1 X 1 2 X X^2+2 X X 1 1 X X^2 1 X 1 X^2+2 1 1 1 X X 0 X 0 X^2+X+2 X^2 X^2+X X^2+2 X X^2+X+2 2 0 X^2+X+2 X^2 X+2 X^2 X 0 X^2+X X^2+X X^2 X^2+2 X^2+X+2 X X^2+2 X^2+X+2 2 0 X X 0 X+2 2 X+2 0 X^2+2 X^2+X+2 X X^2+2 X^2+2 X X^2+X+2 X X^2 X^2+X X^2 X^2+X+2 X^2 X^2+X 0 X^2 X 2 X X^2+X+2 X+2 0 2 X^2 0 X X+2 X^2 X^2+X X^2+X 2 X^2 2 X^2+X 2 X X^2+X+2 X X+2 X^2+2 X^2 0 X+2 X X^2+X 0 X+2 X 0 X+2 X 0 X^2+X 0 0 X^2+2 0 X^2 2 0 0 X^2 0 X^2 X^2+2 2 X^2+2 X^2 X^2+2 0 X^2 2 2 X^2 X^2+2 2 X^2 0 X^2+2 0 2 X^2 2 X^2 X^2 2 0 X^2+2 X^2 0 2 X^2 X^2 X^2 0 0 X^2+2 0 0 X^2+2 X^2+2 X^2+2 0 2 X^2 X^2+2 X^2+2 2 2 2 X^2+2 X^2+2 X^2+2 X^2+2 2 0 X^2 X^2 2 2 X^2 X^2 X^2 2 0 0 2 X^2+2 2 0 0 2 X^2+2 X^2 2 0 X^2 X^2 X^2+2 0 0 0 0 X^2+2 0 0 2 X^2+2 0 X^2 X^2 X^2 X^2 2 X^2+2 X^2+2 2 X^2 X^2+2 X^2+2 X^2 0 0 2 0 X^2+2 X^2+2 X^2 2 0 X^2 0 2 0 0 2 X^2+2 2 X^2+2 X^2 2 X^2 X^2+2 2 X^2+2 X^2 0 X^2 X^2 0 X^2 0 2 0 0 X^2+2 X^2+2 X^2 0 X^2 X^2+2 2 0 X^2 2 X^2 2 X^2+2 X^2 2 X^2+2 2 X^2+2 X^2 2 X^2 0 X^2 X^2 X^2+2 0 X^2 2 X^2+2 X^2 0 2 0 0 0 0 2 2 2 2 0 0 0 2 2 2 2 0 0 2 0 2 2 0 0 2 2 0 0 2 2 2 0 0 2 2 2 0 0 0 0 2 2 0 2 2 0 2 0 0 2 2 0 2 2 2 2 0 2 0 2 0 2 2 2 0 0 0 0 2 2 0 0 2 2 0 0 0 0 0 2 2 2 2 2 2 0 2 0 generates a code of length 87 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 81. Homogenous weight enumerator: w(x)=1x^0+170x^81+91x^82+342x^83+279x^84+370x^85+675x^86+386x^87+656x^88+334x^89+265x^90+236x^91+48x^92+130x^93+11x^94+52x^95+6x^96+16x^97+12x^98+6x^99+4x^101+2x^102+2x^103+1x^104+1x^140 The gray image is a code over GF(2) with n=696, k=12 and d=324. This code was found by Heurico 1.16 in 62.8 seconds.