The generator matrix 1 0 1 1 1 X+2 1 1 2 1 X 1 1 1 X+2 0 1 1 0 1 1 1 1 X 1 1 2 X 1 X 1 1 X 1 2 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 1 1 1 0 1 1 0 1 0 1 1 1 X 1 2 1 1 X 0 2 2 1 X+2 X 1 X 1 1 0 0 1 1 1 0 1 1 0 X+3 1 X X+3 1 3 1 0 1 X+2 1 1 X 1 1 X+1 2 X+3 X+2 1 X 3 1 1 1 1 X 2 1 X+1 1 X+1 2 X+1 1 3 2 X+3 0 1 0 2 X+2 X X 0 2 1 1 X+3 X+2 X+2 1 1 X+1 X+2 1 1 1 2 3 3 1 X+1 1 X+1 0 1 1 1 1 2 1 1 0 X+2 X+3 X 1 0 3 X+2 X+2 0 0 X 0 X+2 0 0 2 2 0 2 X 0 X X X X X+2 X 0 X+2 X+2 0 X X+2 X+2 X 2 0 X+2 0 X+2 2 0 X X+2 2 X+2 2 X X+2 0 X+2 2 X 2 X+2 0 0 2 X X X 0 X+2 X+2 0 2 2 0 0 X 2 0 2 2 2 2 X+2 X X+2 X+2 0 2 X X+2 0 0 2 X+2 0 X+2 X 0 X X 0 0 0 0 X 0 0 X X+2 X+2 2 X X X+2 X+2 X X 2 X 0 0 2 X 2 2 X+2 X+2 X X+2 X 0 X 2 2 0 X+2 X X+2 0 X 0 0 X X+2 0 X 0 X+2 2 2 X 0 0 X+2 2 X+2 2 X X 0 0 X+2 0 0 X+2 0 X+2 2 2 X 2 2 X+2 2 X 2 X+2 2 X X+2 X+2 2 0 2 X 0 X X 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 0 0 0 2 2 0 0 0 2 2 0 0 0 2 0 2 2 2 0 0 2 0 2 0 2 2 2 2 0 2 0 2 2 2 2 0 0 2 2 2 0 0 2 0 2 0 2 2 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 2 2 2 2 2 0 2 0 2 0 2 0 2 2 0 0 0 0 0 0 2 2 0 2 2 0 2 0 2 0 0 0 0 0 0 2 0 0 0 2 0 2 2 0 2 2 2 2 2 0 0 0 2 0 2 0 2 0 0 2 2 2 2 2 2 0 0 0 2 2 0 2 0 0 2 2 0 2 2 0 0 0 2 0 2 2 2 0 0 2 0 2 0 2 2 2 0 0 0 0 2 2 2 2 2 0 0 2 0 0 2 0 2 0 2 0 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+142x^78+64x^79+413x^80+264x^81+634x^82+436x^83+727x^84+472x^85+785x^86+548x^87+714x^88+584x^89+668x^90+412x^91+444x^92+200x^93+310x^94+76x^95+132x^96+16x^97+52x^98+45x^100+19x^102+12x^104+14x^106+6x^108+2x^116 The gray image is a code over GF(2) with n=348, k=13 and d=156. This code was found by Heurico 1.16 in 6.78 seconds.