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 X^2 1 1 1 X 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X^2 1 1 1 1 0 X^2+2 0 X^2+2 0 X^2+2 0 X^2+2 0 X^2+2 X^2+2 0 X^2+2 0 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 0 2 X^2 X^2+2 0 2 X^2 X^2+2 0 2 X^2 0 2 X^2+2 X^2 X^2+2 X^2 0 2 2 0 X^2+2 X^2 0 2 X^2+2 X^2 X^2+2 X^2 2 0 2 X^2 0 2 2 2 2 0 2 X^2 X^2+2 X^2 X^2+2 X^2 0 2 0 2 X^2 X^2 X^2+2 X^2 X^2+2 X^2 0 0 0 2 0 0 0 0 0 0 0 0 2 0 2 2 0 0 0 0 0 0 0 0 0 2 0 2 0 2 0 2 0 2 0 0 2 2 2 2 2 2 0 0 2 2 2 2 2 2 2 0 0 2 2 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 2 2 0 0 0 2 2 0 0 2 2 0 0 2 2 2 2 0 0 0 0 2 0 0 0 2 0 0 0 0 2 0 0 2 0 0 0 0 0 0 0 0 0 2 0 2 0 2 0 2 2 2 2 2 0 2 2 0 2 2 2 2 2 2 0 0 2 2 2 2 2 2 0 0 2 2 2 2 0 0 0 2 2 2 0 0 0 0 0 2 2 2 2 2 2 2 2 2 0 0 0 0 0 2 0 0 2 0 0 0 0 2 0 0 0 2 0 0 0 0 2 2 0 0 2 0 2 2 2 2 2 0 2 0 2 2 2 2 2 0 2 0 0 2 0 2 2 0 2 2 0 2 2 0 0 2 2 0 0 0 0 2 2 0 2 2 2 0 0 0 0 2 0 2 2 2 2 2 2 0 2 2 0 2 2 2 0 0 2 2 0 0 0 0 0 2 0 0 0 0 0 2 0 2 0 0 2 0 2 0 0 0 2 2 2 2 2 0 2 0 2 2 2 2 2 0 2 0 0 0 0 2 0 0 0 2 2 2 2 0 2 2 2 0 2 0 2 2 2 2 2 0 0 0 2 0 0 2 0 0 0 0 2 0 2 0 2 0 0 0 0 0 0 2 2 2 2 0 0 2 2 0 0 2 0 0 0 0 0 0 0 2 0 2 2 2 2 2 0 2 2 2 0 0 2 0 2 2 0 2 0 0 2 0 2 2 0 0 0 0 0 0 0 0 2 2 2 0 2 2 0 2 0 0 2 0 2 0 2 0 2 2 2 2 0 2 0 0 2 2 2 2 0 0 2 2 2 0 0 2 0 0 0 0 0 0 0 2 2 2 0 0 2 0 generates a code of length 89 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 84. Homogenous weight enumerator: w(x)=1x^0+100x^84+82x^86+642x^88+640x^89+314x^90+128x^91+43x^92+22x^94+45x^96+30x^98+1x^172 The gray image is a code over GF(2) with n=712, k=11 and d=336. This code was found by Heurico 1.16 in 61.8 seconds.