The generator matrix 1 0 0 0 1 1 1 1 2 1 1 1 X^2+X+2 X X+2 1 X^2 1 X^2+2 1 1 X^2+X+2 0 1 X^2+2 1 1 X^2+X X^2+X+2 1 1 1 X+2 1 1 1 1 1 2 0 X^2+X+2 X^2+2 X^2+2 X^2+2 1 X 1 1 X+2 1 1 X 1 1 X+2 1 X^2+X 1 X 1 1 1 1 1 1 X^2+X X^2+2 1 X^2 X^2+X+2 X^2+2 0 1 0 X^2+2 X^2+2 1 X^2+X+2 X^2+2 1 1 1 0 1 0 0 0 X^2+3 X+3 X^2+1 1 2 X X^2+X+1 1 1 X X^2 1 X 1 X+3 X^2+X+3 0 1 X+1 1 1 X+2 X^2 X^2+X X X^2+3 X^2+X+3 1 X^2+X X^2+X 3 X^2+2 X^2+1 1 X+2 1 1 1 X^2 1 1 X^2+X+3 X^2+X+1 X^2+X+2 X^2+X+3 1 1 0 X+2 X^2 X^2+2 1 X^2 X^2+2 X+1 X^2+X X^2 X X^2+1 1 X 1 3 1 1 X+2 X^2+X+2 X+1 X 1 X^2 X+3 1 1 X^2+X 1 X^2+X+2 0 0 1 0 X^2 2 X^2+2 X^2+1 3 X^2+3 X^2+1 1 3 2 1 X^2+X+3 X+1 0 0 X^2+1 X+2 X+2 X^2+3 1 X+2 X X+2 1 1 3 X X^2+X+3 X+3 X+1 X+2 X^2 X^2+2 X+1 X^2+3 1 X+1 0 X^2+X+2 1 X^2+X+1 X^2+X X^2+X+1 X^2+X X^2+X+2 0 X^2+X+2 X^2+3 X+3 X^2+X+2 1 X+2 X^2+2 X+1 1 X^2+X+2 1 3 X^2+X+2 X+1 2 1 0 0 X^2+2 X^2+3 1 1 X^2+X 0 X+3 X+2 X^2+X+2 X^2+2 1 1 X^2+X+1 X^2+X 0 0 0 1 X^2+X+1 X^2+X+3 2 2 X+1 X^2+X+1 X^2 X+1 X^2+X+2 3 X^2+X+3 X^2+X+2 X^2+X+1 X+2 1 X^2+X 0 1 X^2+X+2 1 X^2+X+2 X+3 X^2+X+1 3 X^2+X X^2+1 1 X^2+X+3 X X^2+2 X^2+X X^2+X+2 X^2+3 X^2+X+2 1 X^2+X+3 X^2+X+1 X+2 X^2+3 X+2 1 X^2+X X^2+2 X^2+X 1 3 X+2 X^2+3 X^2+1 3 2 X+2 X^2+X+1 X^2+X+3 X+3 X^2+3 X+1 0 X+3 X X^2+X+3 2 X^2+X X^2+2 2 X X^2+X+2 X^2+X X+3 1 X+3 1 X^2 X^2+1 X+1 3 X+3 X+2 0 0 0 0 2 0 2 0 0 0 2 2 2 2 2 2 0 0 2 0 2 0 2 2 0 0 2 0 0 2 2 0 2 0 2 0 0 2 0 2 2 0 0 2 0 0 2 2 0 0 2 2 2 0 0 0 0 0 0 2 0 2 0 0 2 2 2 0 2 0 2 0 2 2 2 2 0 0 2 0 2 2 generates a code of length 82 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 74. Homogenous weight enumerator: w(x)=1x^0+398x^74+1688x^75+3382x^76+5256x^77+7972x^78+11120x^79+12754x^80+14904x^81+16250x^82+14752x^83+14064x^84+10672x^85+7476x^86+4876x^87+2738x^88+1548x^89+600x^90+384x^91+120x^92+64x^93+20x^94+12x^95+11x^96+4x^97+4x^98+2x^100 The gray image is a code over GF(2) with n=656, k=17 and d=296. This code was found by Heurico 1.16 in 187 seconds.