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 X 1 X 1 1 X X X^2 0 X^2+2 0 X^2 0 0 X^2 X^2+2 0 0 X^2 X^2+2 0 0 X^2 X^2+2 0 0 X^2 X^2+2 0 0 X^2 X^2+2 2 X^2+2 2 X^2 2 X^2+2 0 X^2+2 2 2 X^2+2 X^2+2 X^2+2 2 2 X^2 0 X^2+2 X^2+2 2 0 X^2 X^2 2 2 X^2 2 X^2 0 X^2+2 X^2+2 2 2 0 X^2+2 X^2+2 2 0 X^2+2 X^2+2 X^2 2 0 X^2 X^2 X^2 2 X^2 0 2 X^2 0 X^2 X^2 0 X^2+2 0 X^2 X^2+2 2 2 2 2 2 X^2 0 0 X^2+2 X^2 0 X^2+2 X^2 0 X^2+2 0 X^2 0 0 X^2+2 X^2 0 0 X^2+2 X^2 0 0 X^2+2 X^2+2 2 2 X^2 X^2 0 2 X^2 X^2 2 0 X^2 X^2+2 2 X^2 X^2 0 2 X^2 X^2 2 2 X^2 2 X^2+2 0 X^2+2 2 2 X^2+2 2 2 X^2+2 X^2+2 2 X^2 X^2+2 0 X^2+2 0 0 X^2+2 X^2+2 X^2+2 2 2 X^2+2 0 0 2 2 X^2+2 X^2+2 X^2 0 X^2 X^2+2 X^2 2 X^2 X^2 X^2 X^2 X^2 2 X^2 X^2 0 0 0 2 0 0 2 0 0 0 2 0 0 0 2 0 2 2 0 2 2 2 0 2 2 0 2 2 2 0 2 2 2 2 0 0 2 0 0 0 0 0 2 0 0 2 0 0 2 0 0 2 2 0 2 0 2 2 2 2 2 2 2 0 2 0 2 0 2 2 0 2 2 0 0 2 0 0 2 0 0 2 2 2 2 0 0 0 0 0 0 0 0 2 0 2 2 2 0 2 0 2 2 0 2 2 2 0 2 2 2 0 2 0 2 0 0 0 2 0 0 2 2 0 0 2 2 0 2 2 0 2 0 0 0 2 2 0 0 2 0 0 2 0 0 2 2 2 2 0 0 0 2 2 2 0 2 0 2 2 0 2 0 2 2 0 0 0 0 0 0 0 2 0 0 0 2 0 0 0 0 0 0 2 0 0 2 2 2 2 2 0 2 2 0 0 0 0 2 2 2 2 2 0 2 0 0 2 0 2 2 0 0 2 2 0 0 0 2 2 0 2 2 0 2 2 0 0 0 0 0 2 2 0 0 2 0 2 2 2 2 0 0 0 2 2 2 2 0 2 0 2 0 0 2 2 2 0 0 2 0 0 0 2 2 2 2 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+154x^84+32x^86+621x^88+512x^89+480x^90+184x^92+57x^96+6x^100+1x^168 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 3.45 seconds.