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 X 1 X X X 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 X X^2 X X X^2 X 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 2 X^2+2 X^2 0 X^2+2 2 X^2 2 X^2+2 X^2 2 0 X^2+2 2 X^2+2 X^2 X^2+2 X^2+2 X^2 0 X^2+2 X^2+2 0 X^2 0 X^2+2 2 X^2 X^2 0 2 2 0 X^2+2 X^2+2 X^2 0 2 0 X^2 0 2 2 X^2+2 X^2 0 0 2 2 0 2 X^2 0 X^2+2 X^2+2 X^2+2 X^2 0 X^2 2 2 X^2 X^2+2 0 2 X^2+2 2 0 X^2+2 X^2+2 X^2+2 X^2+2 X^2+2 X^2+2 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 0 2 2 2 2 2 0 2 2 0 2 2 0 2 0 2 2 0 2 0 2 0 2 0 2 0 0 2 2 2 0 2 0 2 0 2 2 2 2 2 0 0 2 2 2 2 0 2 2 0 0 2 2 2 0 0 0 0 2 0 0 0 2 0 0 0 0 2 2 2 2 2 2 0 2 2 0 2 2 0 2 2 0 2 0 2 2 0 2 0 0 0 2 0 2 0 2 2 0 2 2 0 2 0 2 0 0 0 2 0 0 2 2 0 0 2 0 2 2 0 0 2 2 0 0 0 2 2 2 2 2 2 0 0 0 2 2 0 0 0 2 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 0 0 0 0 0 0 2 0 2 2 2 2 0 2 2 0 2 2 2 2 2 2 0 0 2 2 0 2 0 2 2 0 0 0 0 2 2 2 2 0 2 2 0 0 2 2 0 2 0 0 2 0 2 0 2 0 2 0 0 2 0 2 0 2 0 2 0 0 0 0 0 2 0 2 2 0 2 2 2 2 2 0 0 0 2 2 0 2 0 2 0 2 2 0 0 2 0 0 2 0 0 0 2 0 2 2 0 0 0 2 2 0 2 2 0 2 0 0 2 0 0 2 0 0 2 0 2 0 2 0 2 0 2 2 0 2 0 2 2 0 2 0 2 2 0 0 2 2 2 0 0 0 2 2 2 0 0 0 0 0 0 0 0 2 0 2 2 2 0 2 0 2 2 0 2 0 0 0 2 2 2 2 2 0 2 2 0 0 2 2 0 0 2 0 0 2 0 2 2 0 2 2 2 0 2 0 2 2 0 0 2 2 2 2 0 0 2 0 0 2 0 2 0 0 0 0 2 0 0 2 0 2 0 0 0 0 2 0 0 2 0 0 2 2 0 2 2 2 generates a code of length 91 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 85. Homogenous weight enumerator: w(x)=1x^0+80x^85+45x^86+32x^87+162x^88+112x^89+312x^90+576x^91+312x^92+112x^93+147x^94+32x^95+34x^96+80x^97+7x^102+2x^104+1x^110+1x^160 The gray image is a code over GF(2) with n=728, k=11 and d=340. This code was found by Heurico 1.16 in 135 seconds.