The generator matrix 1 0 0 0 0 1 1 1 2 1 1 0 1 X+2 1 X+2 X+2 1 2 0 0 1 X 1 1 X+2 0 1 1 1 1 1 X+2 X+2 X+2 1 X 2 1 1 0 2 0 1 0 X X 1 1 1 1 2 X 1 1 1 1 0 1 X+2 1 1 1 2 2 1 X X X+2 1 1 1 1 1 0 1 X 0 1 2 X+2 0 1 X+2 X 1 1 X 1 0 1 0 0 0 0 0 0 0 1 1 1 3 1 X+3 1 2 2 1 1 2 X 1 2 X+1 1 X 3 X+2 X+1 X+2 X+2 1 X 1 1 1 1 3 X+2 X 1 2 0 0 0 X X+1 3 0 3 1 1 3 X X+1 X+2 1 X X X+2 0 1 0 X 3 2 2 2 0 1 X+1 3 X+3 1 1 1 1 X+2 X+2 X+2 X+2 3 0 X X+3 0 1 2 0 0 1 0 0 0 1 1 1 3 1 2 X 1 X+2 X+3 1 X+2 X+1 X 1 3 X+1 2 0 0 X 1 3 1 X X X+3 2 2 0 3 X+2 X+2 1 1 X X+2 1 1 2 1 X X+1 X 1 X+1 X+3 X+2 3 0 1 0 0 1 X+3 2 X 1 2 2 1 X 1 0 1 X+2 X+3 3 X+2 2 X+3 3 X+1 X 2 1 3 1 0 3 X+1 1 2 0 0 0 1 0 1 1 0 3 2 X+1 X+3 X+2 3 3 2 X+1 X X 1 0 X+1 1 X+1 X+2 X+2 1 X+2 2 X+3 1 X 2 0 1 0 3 X 3 X 0 3 1 X 3 1 X+1 X+1 X X+3 2 X+3 1 0 X+3 1 3 0 0 X X+3 X 1 X+3 0 X+1 0 1 X+2 X+2 X+3 2 X+2 1 X+1 0 X+1 3 X+1 1 1 X+1 X X+2 1 X+1 X+1 X+3 1 0 0 0 0 1 1 2 3 1 0 X+1 X+3 X+1 0 0 X+1 2 1 2 2 X+3 3 3 X X 1 1 1 X 2 X+3 1 X 1 X+3 X+1 3 3 X+1 3 3 X 3 2 X+1 2 X 0 X X+2 3 0 X+1 X+2 0 0 1 X X+3 X X+1 X 2 0 1 X+2 1 2 X+3 3 0 X X+1 X+1 1 3 X+2 X+1 X+2 2 2 0 X+2 1 1 X 0 X+2 2 0 0 0 0 0 2 0 2 2 0 2 2 2 0 0 2 0 2 0 0 2 2 2 0 0 2 2 2 0 0 2 2 0 2 2 2 2 2 0 0 0 2 0 2 0 2 2 2 2 2 0 2 0 2 2 2 0 2 0 0 0 2 2 2 0 0 0 2 2 0 2 2 0 2 0 0 0 0 2 2 2 2 2 0 0 2 0 0 0 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+288x^78+714x^79+1138x^80+1616x^81+2145x^82+2696x^83+3405x^84+3868x^85+4244x^86+4868x^87+5162x^88+5240x^89+5010x^90+5010x^91+4724x^92+3886x^93+3299x^94+2754x^95+1854x^96+1314x^97+1056x^98+526x^99+318x^100+182x^101+73x^102+62x^103+33x^104+22x^105+9x^106+8x^107+5x^108+4x^110+2x^111 The gray image is a code over GF(2) with n=356, k=16 and d=156. This code was found by Heurico 1.13 in 88.2 seconds.