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 X 2 X X X 1 X X X X 1 1 1 1 0 X 1 X 1 2 1 X 1 1 1 1 1 0 2 1 0 1 1 1 0 1 X 1 X 0 2 X X 2 1 0 X 0 0 0 0 0 0 0 X+2 X X X X X+2 X 2 X 0 2 0 2 2 X 2 2 X+2 0 0 X+2 X+2 X 0 0 X X+2 X+2 X X 2 0 2 X+2 X 0 X+2 X 0 0 X 0 2 2 X X X 0 X 0 X+2 0 2 2 X X 2 2 X X 0 X X X+2 X+2 0 2 2 X 2 0 2 0 0 X 0 0 0 X X+2 X 2 X X+2 0 0 X 2 X X 2 2 X+2 X+2 0 X X+2 2 X X+2 X+2 0 2 X+2 X+2 2 2 X+2 X+2 X+2 X+2 X+2 2 2 X 2 X+2 0 X X+2 X 0 X X+2 X+2 2 0 0 0 2 0 2 2 0 2 0 0 2 X X X 0 2 X X 0 2 0 0 X 0 X 2 0 0 0 X 0 X X X 0 X+2 2 X X+2 0 0 X+2 X+2 X X+2 2 0 2 X 0 X 2 X X+2 0 2 2 0 2 2 X X X+2 0 2 2 2 X 0 X X X 0 2 X X 2 X+2 0 X+2 X 2 X 2 2 0 2 X X+2 X 2 X+2 X+2 X+2 X+2 X+2 2 0 X+2 2 X 2 0 X 0 0 2 0 0 0 0 X X 0 X X+2 X 0 X 2 X+2 X 2 0 0 0 X+2 X 2 X+2 X X+2 2 X+2 0 0 X 2 2 2 0 X 2 0 2 0 X X+2 0 X 2 0 X+2 0 X X+2 2 2 0 0 0 X X X+2 X X+2 X X+2 X X+2 2 0 0 2 2 X 2 0 0 X+2 X+2 0 X X X X X+2 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 2 2 2 2 0 2 0 2 2 2 2 2 0 0 2 2 0 2 0 0 2 2 2 2 0 0 2 0 2 0 0 2 2 0 2 0 2 2 2 0 0 0 2 2 0 0 0 0 2 2 2 0 2 2 0 0 0 0 2 2 2 0 0 0 0 0 0 0 0 0 2 0 2 0 2 2 2 2 2 0 0 2 0 2 2 2 2 0 0 0 0 0 0 2 2 2 2 2 0 2 0 0 2 0 2 2 0 2 2 0 0 0 2 0 0 0 2 0 2 0 0 2 2 0 0 0 2 0 0 2 2 2 0 2 2 2 0 2 2 0 0 2 2 2 2 generates a code of length 81 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 70. Homogenous weight enumerator: w(x)=1x^0+25x^70+126x^71+191x^72+196x^73+317x^74+318x^75+445x^76+480x^77+469x^78+590x^79+700x^80+704x^81+538x^82+664x^83+542x^84+440x^85+377x^86+250x^87+195x^88+164x^89+143x^90+70x^91+83x^92+56x^93+41x^94+26x^95+16x^96+8x^97+10x^98+4x^99+2x^100+1x^112 The gray image is a code over GF(2) with n=324, k=13 and d=140. This code was found by Heurico 1.16 in 7.47 seconds.