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 X 1 1 1 X^2 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 0 X^2+2 0 X^2+2 0 X^2+2 0 X^2 2 X^2+2 X^2+2 0 0 X^2+2 X^2 2 0 X^2+2 X^2 2 0 X^2+2 2 X^2 0 X^2+2 2 X^2 0 X^2+2 2 X^2 0 X^2+2 X^2 2 0 X^2+2 0 X^2+2 X^2 0 2 X^2+2 2 X^2 X^2+2 2 2 X^2+2 2 X^2 0 X^2+2 0 X^2+2 X^2+2 0 X^2 0 2 2 0 2 X^2+2 X^2 0 2 2 2 0 0 0 2 0 2 X^2+2 X^2 X^2+2 X^2+2 X^2 X^2+2 X^2 X^2+2 0 X^2 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 2 0 2 2 2 2 0 0 0 0 2 2 2 2 2 2 2 2 0 0 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 2 2 0 2 0 2 0 2 0 2 2 0 2 0 0 0 0 0 0 2 2 2 2 0 0 2 0 0 2 0 2 2 2 0 0 0 0 2 0 0 0 2 0 0 0 0 0 2 2 0 0 2 2 0 2 0 2 0 2 0 2 0 2 0 0 2 0 2 0 2 2 2 2 0 2 0 2 0 0 2 2 2 2 2 2 2 2 2 2 0 0 0 2 2 0 0 0 2 0 0 2 2 0 0 0 0 2 2 0 0 2 0 2 2 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 0 2 0 2 2 2 2 0 0 2 2 2 2 0 0 0 2 2 2 0 0 0 2 2 0 2 0 2 2 2 2 0 0 0 2 2 2 0 0 0 0 2 2 2 2 2 0 2 2 2 2 0 2 2 0 2 2 0 0 0 2 0 0 2 0 0 0 0 0 0 0 2 0 2 0 0 2 2 2 2 0 2 0 2 0 2 2 2 2 0 0 2 0 0 0 2 2 2 2 0 0 0 0 0 0 0 0 2 2 2 0 0 2 0 2 0 2 2 2 2 2 2 2 0 2 2 2 0 0 0 0 0 0 0 0 0 2 2 0 2 0 2 2 2 2 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 2 2 2 2 0 2 2 2 2 0 2 0 0 0 2 2 0 0 2 2 0 2 0 2 2 0 0 2 2 0 0 2 0 2 2 2 2 2 0 0 2 2 0 2 0 2 0 2 0 2 0 2 0 0 0 2 0 0 2 2 0 2 0 2 2 0 2 2 2 0 2 2 0 0 2 0 0 0 0 generates a code of length 87 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 80. Homogenous weight enumerator: w(x)=1x^0+15x^80+34x^81+30x^82+46x^83+50x^84+156x^85+74x^86+1182x^87+301x^88+24x^89+18x^90+26x^91+14x^92+20x^93+6x^94+26x^95+2x^96+22x^97+1x^168 The gray image is a code over GF(2) with n=696, k=11 and d=320. This code was found by Heurico 1.16 in 0.907 seconds.