The generator matrix 1 0 0 0 0 1 1 1 1 2 1 2 X+2 1 X 1 1 X 1 1 2 1 1 2 X+2 2 1 1 1 1 0 2 1 X+2 1 2 1 1 1 X+2 1 0 1 0 1 X 1 1 X 1 1 1 1 X+2 X+2 1 1 X+2 0 X 1 1 2 2 X+2 1 X+2 0 0 X+2 0 1 X+2 1 1 0 1 1 0 1 0 0 0 0 X+1 2 X+3 1 2 X+2 1 X+1 X+2 3 X 1 3 3 1 2 2 1 1 1 0 2 X+1 X+3 X X X+3 1 X+1 2 X 2 X+2 2 X+3 1 X+2 1 X 1 X+3 1 1 2 X+3 X+2 1 1 X 2 3 X+2 X+2 1 2 1 1 2 X X+1 1 1 0 1 1 3 2 2 X 2 X+1 0 0 0 1 0 0 0 1 3 2 X+1 X+1 1 X+2 X+3 1 0 3 X X+1 X+2 X+1 X+3 X 3 1 0 3 X+2 1 X X 1 X+1 X+2 X+1 X+2 X 0 1 1 0 1 0 2 2 2 X+3 X+3 1 X+1 X+2 3 0 0 X+2 1 1 1 1 X+3 3 X+3 1 1 1 2 X X+2 1 2 X+2 2 0 X 1 2 0 0 0 0 0 1 0 1 2 1 3 X+1 X X+3 X+3 1 0 X 0 X+2 X+1 X+2 3 3 X+3 X+2 0 1 1 X+2 2 3 1 X+1 X+1 3 X 1 X X+1 0 1 X X+1 2 0 X+3 2 X+3 2 2 X+2 X+1 X+3 3 X+3 1 X+3 1 X X+3 3 2 1 0 1 0 X+2 X+3 1 1 0 1 0 1 X+3 3 1 X+2 2 0 0 0 0 1 1 3 0 2 X+3 X+1 1 X X+3 3 1 0 1 X+2 0 2 3 0 X X+1 X+3 X 1 X 1 X+1 0 X+1 X+1 3 X+3 X+1 3 X+3 3 X X+2 X+2 0 2 3 X 2 X 0 X+3 2 1 0 0 3 2 3 X+1 3 X+3 3 1 X+2 2 3 1 3 X X+2 0 X+3 X+1 1 X+3 X+3 X+1 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 2 X+2 X X X+2 X X+2 X X+2 X X X X+2 X+2 X X+2 X X X+2 X+2 X X 2 X+2 X X X X 2 2 2 X X+2 X X X 2 X+2 0 generates a code of length 78 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 66. Homogenous weight enumerator: w(x)=1x^0+113x^66+444x^67+1165x^68+1760x^69+2622x^70+3704x^71+4872x^72+6346x^73+7558x^74+9154x^75+10467x^76+11088x^77+11739x^78+11656x^79+10563x^80+9450x^81+7992x^82+6386x^83+4891x^84+3392x^85+2295x^86+1478x^87+880x^88+498x^89+263x^90+128x^91+81x^92+40x^93+24x^94+10x^95+8x^96+2x^97+2x^98 The gray image is a code over GF(2) with n=312, k=17 and d=132. This code was found by Heurico 1.13 in 273 seconds.