The generator matrix 1 0 1 1 1 X+2 1 1 2 1 X 1 2 1 1 1 X+2 1 X 1 1 1 1 X 0 1 1 1 X 1 0 1 1 0 1 1 1 0 1 1 1 1 2 X 1 1 1 1 X 1 1 0 1 0 X+2 1 1 1 X+2 2 1 2 1 1 1 1 0 1 1 2 1 2 0 1 0 1 0 1 X 0 1 0 1 1 0 1 1 X X+3 1 X+2 1 X+3 1 0 X+1 3 1 2 1 X+2 3 1 0 1 1 X X+1 X 1 X+1 1 X+1 2 1 3 2 3 1 3 1 0 X+2 1 1 X+3 X X+1 X+1 1 0 X+3 1 2 1 1 2 0 X+3 1 1 0 1 X+2 X+1 0 2 1 X+3 X+2 0 X+1 1 1 X 1 X+2 2 X+2 0 1 0 0 0 X 0 0 0 0 0 0 2 2 X+2 X X 2 X X X X+2 X 2 X X X+2 2 2 0 0 2 X X X 2 X 0 0 0 2 0 X+2 2 2 X+2 X+2 X X+2 X+2 0 X X 2 X+2 0 X+2 X X+2 X X+2 X 2 0 2 X 0 0 0 0 2 X+2 2 2 2 X 0 X X 0 0 0 2 0 0 0 0 X 0 0 X 2 X 2 X+2 2 X+2 2 X X+2 0 X X 0 0 0 X+2 0 2 0 X X+2 X+2 0 0 X+2 0 X+2 X+2 X+2 X 0 2 X 2 X+2 2 X+2 X+2 X 0 X 0 X X+2 2 X+2 X+2 X+2 0 X+2 2 X+2 X 0 X 2 X+2 2 0 X X+2 2 X 0 X X+2 X+2 0 0 X X X X+2 0 0 0 0 0 X 0 0 X+2 2 0 2 2 X+2 X X+2 2 X X X X 2 X+2 2 0 X X+2 0 X+2 X+2 X+2 X 0 X 0 2 X+2 X+2 X+2 0 X 0 2 2 X+2 X+2 X+2 2 X X+2 X 0 2 X 2 2 X 0 X 2 X+2 X+2 2 2 X 0 2 0 X+2 2 X X+2 2 X 2 2 X+2 0 2 X+2 X+2 0 0 0 0 0 0 2 0 0 2 0 2 0 2 0 0 0 2 0 2 0 2 2 2 0 0 2 2 2 0 2 2 2 0 2 0 0 2 2 0 0 2 2 2 0 2 0 2 2 0 2 0 2 0 0 2 2 0 0 0 2 0 0 0 0 0 2 0 0 0 2 0 0 2 2 0 2 2 2 0 2 0 0 0 0 0 0 0 2 2 0 2 2 2 2 0 0 2 2 2 0 2 0 0 0 0 0 2 0 2 0 2 0 2 0 0 0 2 2 2 2 0 0 0 0 0 2 0 2 0 2 0 2 2 0 2 2 0 2 2 0 0 2 0 0 2 2 0 2 2 0 2 0 2 2 0 0 2 2 2 2 2 0 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+77x^70+120x^71+216x^72+358x^73+456x^74+682x^75+848x^76+1078x^77+1104x^78+1174x^79+1422x^80+1432x^81+1479x^82+1250x^83+1133x^84+1000x^85+710x^86+598x^87+376x^88+284x^89+198x^90+122x^91+78x^92+64x^93+65x^94+18x^95+17x^96+6x^97+3x^98+2x^99+5x^100+2x^101+3x^102+2x^103+1x^110 The gray image is a code over GF(2) with n=324, k=14 and d=140. This code was found by Heurico 1.16 in 19.8 seconds.