The generator matrix 1 0 1 1 1 0 1 1 X 1 X+2 1 1 1 0 1 1 1 X 2 1 2 1 1 1 2 1 1 1 1 X 1 X+2 1 1 X+2 1 1 1 X 1 1 0 1 X+2 0 2 1 1 2 1 1 1 1 1 0 1 X 1 2 1 1 1 X 1 1 X 1 1 1 0 2 1 1 1 1 X+2 1 X 1 X 2 X+2 1 0 1 0 2 1 0 1 1 0 1 1 0 X+3 1 2 1 X+3 3 2 1 2 3 X+1 1 1 2 1 0 X+3 1 1 3 0 2 1 1 X+2 1 1 0 1 X+2 X+1 X+1 1 X X 1 2 1 1 1 X+3 X+2 1 1 X 3 X+1 1 1 X+2 1 X+2 1 X+3 X 1 1 X+3 X+2 1 1 X 2 X 1 X+1 X+1 2 X 1 1 0 X+2 1 1 1 X+2 1 1 0 1 1 0 0 X 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 X+2 X X+2 X X X+2 X X X X X X+2 X+2 2 X X+2 0 X X+2 X+2 2 X+2 2 2 X X+2 X X X+2 2 X 0 2 0 X X 0 X+2 2 X 2 0 X+2 0 2 X 0 0 2 2 X X+2 X 2 X+2 X X+2 0 X X 0 0 0 0 0 X 0 0 0 0 2 X+2 2 0 0 2 X X+2 X+2 X X X 0 X+2 X+2 2 X 2 X+2 2 X X 2 X X X+2 2 2 0 2 X+2 X+2 0 X X X 2 X 2 2 0 2 0 X 0 X+2 2 X 2 X+2 2 0 X 2 0 X 0 X X+2 2 X+2 0 2 X+2 X+2 X+2 0 X 2 X+2 2 X 0 2 0 X X 0 X+2 2 2 0 0 0 0 X 0 X 2 X X+2 X X X+2 X 0 2 0 X+2 X+2 X+2 2 0 X+2 0 0 X X X 0 X+2 2 X X 2 0 X X+2 X+2 0 2 X X+2 X+2 2 X 2 X X 0 2 0 X X+2 0 2 0 2 X X 0 X X 2 X 0 0 X 2 2 2 2 X+2 2 2 0 2 0 0 0 X 0 0 X+2 2 X 0 X+2 0 2 0 0 0 0 0 X X+2 X 2 X X+2 X+2 X 0 X+2 X+2 X+2 X+2 2 X+2 X 0 0 0 2 X 0 2 X X+2 0 X+2 X X X 2 X 0 0 X 0 2 0 2 X X 2 0 2 X+2 X+2 2 X+2 X X X X X+2 X+2 X 2 X+2 X+2 X 0 X X 0 2 X+2 X+2 0 X X X 0 0 0 X+2 0 X X+2 2 0 X 2 2 2 X generates a code of length 89 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 78. Homogenous weight enumerator: w(x)=1x^0+42x^78+128x^79+303x^80+384x^81+504x^82+738x^83+755x^84+1038x^85+1196x^86+1216x^87+1375x^88+1414x^89+1319x^90+1098x^91+1145x^92+1018x^93+761x^94+594x^95+418x^96+296x^97+203x^98+144x^99+76x^100+54x^101+51x^102+38x^103+18x^104+18x^105+18x^106+12x^107+2x^108+2x^109+2x^110+1x^112+2x^116 The gray image is a code over GF(2) with n=356, k=14 and d=156. This code was found by Heurico 1.16 in 22.6 seconds.