The generator matrix 1 0 0 0 1 1 1 1 2 1 X+2 X^2+X+2 1 X^2+X 1 1 1 0 1 X^2+X+2 1 1 X^2+X+2 1 X^2+X+2 1 1 2 X^2+X X^2 X^2+X+2 X 1 0 1 X^2+X+2 X 1 2 1 X^2 1 1 X^2+2 2 1 1 X^2+X+2 1 1 X 1 X^2 1 X^2 1 X+2 0 1 1 1 X^2+2 1 1 X+2 0 1 2 X+2 0 1 X X 2 X X^2+2 1 1 0 1 0 0 X X^2+1 2 X^2+3 1 X^2+X+2 X 1 3 1 X^2+X+3 X+1 X^2+2 1 0 1 X^2+X+2 X^2+X+1 1 X^2 X^2 1 X+1 X+2 X^2+X 1 1 1 3 X^2+X X 1 X^2+X+2 X+1 X^2 X^2+X+1 1 0 X^2 1 X^2+X+2 X^2+1 X^2+2 X+2 1 X^2+X 1 X^2+X 1 X^2+1 1 X+2 X^2+2 1 X^2 X^2 X^2+X+3 1 X^2+3 X+2 X+2 X^2 X+1 1 1 1 0 X^2 X^2+2 1 1 X X+2 0 0 0 1 0 0 2 X^2+3 X^2+1 1 X^2+1 1 3 X^2+X+2 X+2 3 X^2+X+2 X+1 X^2+X+1 X X^2+1 X+2 X+3 X^2+2 X^2+X+1 1 X^2+1 X X^2 1 X^2+X+2 X^2+X+1 X^2 X^2+X+1 1 X^2 X+1 1 X^2+X+3 X^2+2 2 1 X^2+2 X X^2 1 X+2 X^2+3 X^2+X+2 1 X+1 1 1 X^2+1 X^2 X^2+2 0 X X+2 X^2+X+3 X^2+2 3 X 3 X+2 X^2 X^2+X X^2+X X^2+X+1 X^2+X X+2 3 1 1 X+3 X+1 1 X^2+3 0 0 0 0 1 1 X+3 X+1 2 X^2+X+3 X+2 X^2+X+1 X^2+X+2 X^2+X X+3 X+1 X^2+3 2 X 3 3 0 X^2 X+1 X^2+X+1 X^2+X 1 X^2+2 1 3 0 X^2+2 3 X^2+2 3 X+1 X+3 X+2 3 1 X^2+X+2 X^2+X+3 X+2 X^2+X+2 X^2+X+3 X^2+X+3 X^2 X^2+X+3 1 X^2+X+2 X X^2+1 X^2+1 X^2+X+2 X+2 0 2 1 X+1 X^2+X+2 1 X^2+3 X^2+X X^2+2 X^2+X+3 1 1 X+1 X+3 2 0 X^2+3 3 0 X^2+2 X X^2+2 2 0 0 0 0 0 2 0 0 0 0 2 2 2 2 2 2 0 2 2 2 0 0 0 2 0 0 2 2 0 2 0 0 2 2 0 0 0 2 0 2 0 2 0 2 0 2 2 2 0 0 2 2 0 2 2 2 0 0 0 0 0 2 0 2 2 0 2 0 0 2 2 0 2 0 0 0 0 2 2 generates a code of length 78 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 70. Homogenous weight enumerator: w(x)=1x^0+287x^70+1412x^71+3269x^72+5176x^73+7887x^74+10580x^75+13402x^76+14952x^77+16854x^78+15832x^79+13481x^80+10794x^81+7677x^82+4304x^83+2625x^84+1422x^85+683x^86+252x^87+115x^88+38x^89+18x^90+4x^91+2x^92+2x^93+2x^94+1x^108 The gray image is a code over GF(2) with n=624, k=17 and d=280. This code was found by Heurico 1.16 in 181 seconds.