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 X^2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X^2 X^2 X 1 1 1 1 X 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 2 X^2 0 X^2+2 2 X^2+2 2 X^2 2 X^2 X^2+2 0 X^2 2 0 X^2+2 0 X^2 2 X^2 2 X^2+2 X^2+2 0 0 X^2 2 X^2 0 X^2 X^2+2 2 2 X^2+2 0 X^2 0 X^2+2 0 X^2+2 2 X^2+2 0 2 X^2+2 X^2 0 2 0 X^2+2 X^2 0 2 X^2+2 X^2 0 2 2 2 X^2+2 X^2 X^2 X^2 0 2 0 2 2 X^2+2 X^2+2 X^2+2 X^2 X^2+2 0 X^2+2 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 2 2 2 2 2 0 0 2 0 2 0 0 2 2 2 2 2 0 2 2 2 0 0 2 2 2 2 2 2 0 0 2 2 0 2 0 2 2 0 2 2 2 0 2 0 0 0 2 2 2 2 0 2 0 0 2 2 0 0 0 0 0 0 2 2 2 2 0 0 0 2 0 0 0 2 0 0 0 0 2 2 2 2 2 0 2 0 0 0 0 0 2 2 2 2 0 0 2 2 2 2 0 0 2 2 0 2 2 0 0 2 0 2 2 0 2 0 2 2 2 2 0 2 2 0 2 0 0 0 0 2 0 0 0 2 0 0 0 2 2 2 2 2 0 2 0 0 2 0 0 2 2 0 2 2 2 2 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 2 2 0 2 2 2 2 2 2 2 2 2 2 2 2 0 0 2 2 2 0 2 0 2 2 0 2 0 2 0 0 2 2 2 0 2 2 2 2 0 0 0 2 0 2 2 2 2 2 2 0 0 0 2 2 0 2 0 2 2 2 2 2 2 0 2 2 2 0 0 0 0 0 0 2 0 2 2 0 2 2 2 2 0 0 2 2 0 2 0 2 0 2 0 2 0 2 2 0 0 2 0 2 2 0 0 2 0 2 2 0 2 2 0 0 2 2 0 2 0 0 2 0 2 2 0 0 0 0 2 0 2 2 0 2 0 2 2 0 2 0 0 2 0 0 2 0 2 2 2 2 2 2 2 0 2 0 0 0 0 0 0 0 0 0 2 0 2 2 2 0 2 0 0 2 2 0 2 0 2 2 2 2 2 0 0 2 0 2 2 0 0 2 2 0 0 2 0 0 2 2 2 0 0 2 0 2 2 0 0 2 0 0 0 2 0 2 2 2 0 0 2 2 0 2 0 2 0 2 2 2 0 0 2 2 2 2 2 0 0 0 2 2 0 2 0 0 0 2 generates a code of length 90 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 84. Homogenous weight enumerator: w(x)=1x^0+62x^84+102x^86+219x^88+320x^89+674x^90+384x^91+106x^92+64x^93+26x^94+43x^96+30x^98+16x^100+1x^168 The gray image is a code over GF(2) with n=720, k=11 and d=336. This code was found by Heurico 1.16 in 1.02 seconds.