The generator matrix 1 0 0 1 1 1 X 1 1 X+2 1 1 X X+2 X X+2 1 1 0 1 1 X+2 1 1 1 1 2 2 1 1 1 1 1 2 1 0 1 2 2 2 X 1 2 1 1 1 1 0 2 1 1 X 1 1 2 X+2 1 1 2 X+2 X+2 1 X X 0 1 X 1 1 1 1 1 2 1 1 1 X+2 1 0 1 0 X 1 X+3 1 X+2 0 2 1 X+1 X+2 1 1 1 X 3 1 0 X+1 1 X+2 0 X+1 1 1 X 2 X+2 X 3 1 X+2 0 1 X 1 1 1 2 X+1 1 X+3 3 1 0 1 1 X+1 2 X+2 X 0 1 1 2 X+3 2 2 X 2 1 1 1 0 1 1 1 X+2 2 X+2 1 0 3 X 1 0 0 0 1 1 X+3 X+2 1 X+3 X+2 1 1 0 1 X+1 X 0 X+2 2 1 X+3 3 X+2 0 3 X+3 X 1 1 X X+1 X+2 0 X+1 1 0 X+3 3 X+1 X X+2 1 3 X+3 X+2 X 3 X+3 1 X 0 X+2 1 X+1 2 X+2 1 1 1 1 1 1 X+1 X 3 0 0 1 2 2 X+2 2 0 X+3 X+1 X X+2 3 0 0 0 0 2 0 0 0 0 2 2 0 0 0 2 2 0 2 0 2 2 2 2 2 2 0 2 0 2 2 0 0 2 0 2 0 0 0 2 0 0 2 0 0 0 0 2 2 2 0 0 2 2 2 0 2 0 2 2 0 0 2 2 0 0 2 2 2 2 0 2 0 2 2 0 2 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 2 2 2 2 2 0 2 0 0 0 2 0 2 2 2 2 0 0 0 0 0 0 2 2 2 2 0 2 0 0 2 0 2 0 2 0 0 0 0 2 2 2 2 0 0 0 2 2 2 0 2 2 0 0 0 0 2 2 0 0 0 2 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 2 2 2 0 2 2 2 2 2 2 0 2 2 2 2 2 0 2 0 0 0 0 0 0 0 2 2 2 0 2 2 0 2 0 2 2 2 0 0 2 2 2 2 0 2 0 0 0 2 0 0 0 2 0 2 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 2 2 2 0 2 2 2 2 2 2 2 0 0 0 2 0 2 2 2 2 2 0 2 0 2 0 2 2 0 0 2 2 0 2 2 2 2 2 2 2 2 0 2 0 2 0 2 0 2 2 2 0 0 2 2 0 2 0 2 0 0 0 2 0 0 0 0 0 0 0 2 2 2 2 2 2 0 0 2 0 0 0 0 0 2 2 2 2 2 0 2 0 0 2 2 2 0 0 0 2 2 2 2 0 0 0 0 2 2 0 0 0 2 0 0 2 0 0 2 2 0 2 0 0 0 2 2 0 2 2 2 2 2 0 0 2 2 2 0 2 0 generates a code of length 78 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+66x^68+174x^69+317x^70+582x^71+543x^72+980x^73+1031x^74+1338x^75+1081x^76+1618x^77+1235x^78+1528x^79+1048x^80+1326x^81+924x^82+924x^83+480x^84+446x^85+279x^86+222x^87+87x^88+60x^89+40x^90+10x^91+21x^92+2x^93+9x^94+4x^95+1x^96+2x^97+4x^98+1x^106 The gray image is a code over GF(2) with n=312, k=14 and d=136. This code was found by Heurico 1.16 in 15.4 seconds.