The generator matrix 1 0 1 1 1 X+2 1 1 0 1 1 X+2 1 1 X+2 1 1 0 1 0 1 1 1 X+2 1 1 0 1 1 X+2 1 1 1 1 X+2 1 1 2 1 1 1 X 1 0 1 1 0 0 X 1 1 2 1 0 1 2 X 1 1 1 1 1 1 1 1 1 2 1 1 X X+2 X 0 1 1 1 1 1 1 1 1 1 X 1 1 X 0 0 1 X+1 X+2 1 1 0 X+1 1 X+2 3 1 0 X+1 1 X+2 3 1 3 1 0 X+2 X+1 1 X+2 X+1 1 0 2 1 3 X+2 X+2 X+1 1 X 0 1 1 X+1 0 1 X 1 X+3 3 1 1 1 3 0 1 2 1 X+3 1 1 X+3 X+1 0 X+2 X 1 3 1 1 1 X+1 X X+2 1 1 1 X+2 X+2 2 X 2 3 3 X+2 X+2 1 X+2 0 0 1 0 0 2 0 0 0 0 0 0 0 0 2 0 2 2 2 2 2 0 2 0 2 0 2 2 0 2 2 2 0 2 0 2 2 0 2 0 0 2 0 2 0 2 2 0 0 2 0 0 2 0 0 2 2 0 2 0 0 2 2 2 2 0 2 0 2 0 0 0 0 0 2 2 2 0 0 2 0 0 2 0 0 2 0 2 0 0 0 0 0 2 0 0 0 0 0 2 0 2 2 0 2 0 2 0 2 0 2 2 0 0 2 0 0 2 0 0 0 2 0 2 2 2 2 0 2 0 0 0 0 2 0 2 2 0 2 0 2 0 2 0 0 2 2 2 2 2 0 0 2 2 0 0 2 0 2 2 2 0 2 2 0 0 2 2 2 2 2 0 0 0 0 2 2 0 0 0 0 2 0 0 0 0 2 2 0 2 2 0 0 2 2 2 2 0 2 2 0 0 2 0 0 2 0 2 0 0 0 2 0 2 2 2 2 2 0 0 2 0 2 0 2 0 0 0 2 2 2 0 0 0 2 2 0 0 2 0 2 0 2 0 0 0 2 2 0 0 2 0 2 2 0 0 2 2 0 2 0 0 2 0 0 0 0 0 0 2 0 0 2 0 2 2 0 0 2 2 2 0 0 2 0 2 2 0 2 2 0 0 0 2 0 2 0 0 2 0 0 0 2 0 0 2 0 2 0 0 2 0 0 2 2 2 2 2 2 0 0 0 0 2 2 2 2 0 2 2 2 0 2 2 0 2 0 0 2 2 0 0 0 2 0 2 2 0 2 2 0 0 0 0 0 0 0 2 0 2 0 0 0 2 0 2 0 2 2 2 2 2 0 0 0 2 2 2 0 2 2 2 2 0 2 2 2 0 0 0 2 0 0 2 0 2 0 2 2 2 2 0 0 0 0 0 2 0 2 0 0 0 2 0 2 2 0 0 2 0 0 0 0 2 2 2 2 2 0 2 2 0 0 0 2 0 0 2 0 0 0 0 0 0 0 2 2 0 2 0 0 2 2 2 2 0 2 0 0 2 0 2 2 0 2 0 0 0 2 0 2 0 2 2 2 2 2 0 0 2 2 0 2 0 0 2 0 2 2 0 0 0 2 2 2 0 0 2 0 0 0 0 0 2 2 0 2 0 2 2 0 2 2 2 0 2 2 0 2 2 2 0 2 0 2 generates a code of length 87 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 78. Homogenous weight enumerator: w(x)=1x^0+40x^78+36x^79+203x^80+128x^81+400x^82+128x^83+460x^84+128x^85+459x^86+184x^87+489x^88+128x^89+438x^90+128x^91+320x^92+128x^93+172x^94+36x^95+48x^96+14x^98+9x^100+5x^102+3x^104+2x^106+2x^108+2x^110+2x^114+1x^116+2x^118 The gray image is a code over GF(2) with n=348, k=12 and d=156. This code was found by Heurico 1.16 in 1.64 seconds.