The generator matrix 1 0 0 1 1 1 X+2 1 2 1 1 X 1 0 1 1 0 1 0 1 2 1 X X+2 1 1 X 1 1 X+2 1 0 2 1 X 1 1 1 X+2 0 1 X+2 1 1 1 X+2 1 0 1 2 1 1 1 X 1 2 0 1 2 1 X+2 1 X+2 1 2 1 0 1 X 1 X 1 1 0 1 X+2 1 1 1 0 1 2 2 X 0 0 2 X+2 1 0 1 0 0 1 X+3 1 3 1 X 2 X 3 1 2 0 1 X+1 X+2 X+3 1 0 X+2 1 3 0 1 3 X 1 X+3 X 1 1 1 X+2 X 3 2 1 0 1 X+3 0 X+3 1 2 1 0 0 3 X+2 2 1 X+1 1 1 3 1 2 1 X X 0 X+2 0 1 X+3 1 2 X+2 1 2 1 2 0 X+3 0 X+1 1 X+2 1 1 X+2 X+2 1 1 1 0 0 0 1 1 1 0 1 X X+1 X+3 X 1 X+3 X 1 X X+3 2 1 3 X X+3 1 X+1 X+1 0 X+2 0 2 0 3 1 X+3 2 X+2 2 3 X+2 1 X+1 X+1 X+1 X+2 X X+3 0 0 0 1 1 2 2 X X X+3 1 0 0 X+2 1 2 1 1 X 1 X+3 X+3 1 2 X 1 1 1 3 2 1 1 X+3 X+1 2 X+3 X+2 1 1 1 3 X 1 0 0 0 0 X 0 0 2 0 2 X 0 0 0 0 0 X+2 X X X+2 X+2 X 2 X+2 X X+2 X+2 X X 0 2 0 2 X+2 2 X+2 0 X X X 2 0 2 0 2 X+2 2 X X+2 0 2 X+2 X+2 X 2 X+2 X X 2 0 X X X X X+2 X+2 X+2 0 0 X+2 0 2 0 2 2 2 X+2 X+2 X+2 0 0 X X+2 0 X X+2 X 0 X 2 0 0 0 0 X X+2 X+2 X+2 X 0 0 2 X X+2 2 2 X X 2 X X 2 2 X+2 X+2 0 X+2 X 2 2 0 X 2 2 2 X+2 X+2 2 X+2 2 X 2 2 X X+2 X X+2 0 X X+2 2 X X+2 X+2 0 2 X+2 X 2 X 2 0 0 X X 2 0 X+2 0 X 0 0 2 X X+2 X+2 X+2 0 0 X X 2 X+2 0 X 0 2 2 2 0 0 0 0 0 2 0 0 2 2 2 2 2 2 2 2 2 2 0 2 0 0 2 0 0 0 2 0 0 2 0 2 2 0 0 0 2 2 0 2 0 0 2 2 2 2 2 2 2 0 2 0 2 2 2 0 0 0 0 2 2 2 0 2 0 2 2 0 0 0 2 2 0 2 2 2 0 0 0 0 2 0 0 2 2 0 2 0 2 generates a code of length 89 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 79. Homogenous weight enumerator: w(x)=1x^0+74x^79+205x^80+486x^81+517x^82+832x^83+804x^84+1118x^85+1011x^86+1420x^87+1201x^88+1544x^89+1087x^90+1416x^91+878x^92+956x^93+692x^94+742x^95+436x^96+390x^97+176x^98+156x^99+105x^100+38x^101+28x^102+20x^103+8x^104+12x^105+8x^106+12x^107+9x^108+1x^110+1x^112 The gray image is a code over GF(2) with n=356, k=14 and d=158. This code was found by Heurico 1.16 in 19.5 seconds.