The generator matrix 1 0 0 1 1 1 0 1 1 2 1 X 1 X+2 1 1 1 X 2 X 1 1 1 1 X+2 1 X+2 2 X 1 1 1 2 2 X+2 0 X+2 1 1 X+2 1 1 1 1 1 1 2 1 2 1 1 1 1 X 2 1 1 2 X+2 1 X 1 1 1 1 1 2 1 X X+2 1 2 2 1 1 1 2 X+2 1 2 1 1 0 1 0 0 1 1 1 2 1 1 X+1 X+2 X+3 1 2 X X+2 1 X 1 X+3 0 X+2 1 0 X+1 1 1 1 1 X 1 X 1 1 1 1 X X 1 X+3 X+1 2 X X+3 3 2 X+1 1 0 X+1 X+2 X 1 1 0 3 1 1 X 1 0 2 3 3 1 2 X+2 1 1 3 1 1 X+1 3 X+3 X+2 1 X+3 1 3 X 0 0 1 X+1 X+3 0 X+1 X 1 X 0 1 X 1 3 2 X+3 X+2 1 X+3 3 X+2 3 X 1 X+1 3 3 2 3 X X 1 X+2 0 3 X X X+1 X+3 X X+3 2 X+1 3 2 1 3 X+2 1 2 X+3 X 0 1 3 X+3 X+1 X+3 3 2 X+3 1 2 3 3 1 1 0 X 0 1 X+3 X+3 X+3 X+1 1 0 2 X+1 0 X 0 0 0 2 0 0 0 2 2 0 2 2 0 2 0 0 0 2 0 2 2 2 0 2 0 0 0 2 0 2 0 0 0 2 2 0 2 2 2 0 0 2 0 0 2 0 2 2 0 2 2 0 2 2 2 0 0 0 0 2 0 2 2 2 2 0 0 2 0 2 2 2 2 0 2 2 2 2 0 2 2 0 0 0 0 0 2 0 0 0 0 0 0 2 2 2 2 2 0 0 2 0 2 2 0 2 0 0 2 0 2 2 2 2 2 2 0 0 2 0 2 2 0 0 2 2 2 0 2 0 0 2 2 2 0 2 0 0 2 0 2 2 0 0 2 2 2 2 2 0 2 2 2 2 2 2 2 0 2 2 2 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 2 2 2 2 0 2 2 2 2 0 0 2 0 2 0 2 0 2 0 0 2 2 2 0 2 2 2 2 2 2 2 0 2 0 0 0 0 2 0 2 2 0 0 2 0 2 0 2 0 2 2 2 0 0 2 2 0 0 0 0 0 0 0 0 2 0 2 2 2 2 0 0 2 2 2 2 2 2 0 2 0 0 2 0 2 0 2 2 0 2 0 0 0 0 2 0 0 0 0 2 0 0 0 2 2 0 0 2 0 2 2 0 2 2 0 0 2 2 0 0 0 2 0 2 0 2 0 2 0 2 2 0 0 0 0 0 0 2 2 2 generates a code of length 82 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 74. Homogenous weight enumerator: w(x)=1x^0+163x^74+180x^75+545x^76+380x^77+746x^78+508x^79+940x^80+552x^81+778x^82+476x^83+666x^84+408x^85+490x^86+324x^87+393x^88+168x^89+193x^90+48x^91+121x^92+28x^93+52x^94+17x^96+10x^98+4x^100+1x^104 The gray image is a code over GF(2) with n=328, k=13 and d=148. This code was found by Heurico 1.16 in 4.99 seconds.