The generator matrix 1 0 1 1 1 X+2 1 1 2 1 1 X 1 1 X X 1 1 0 1 1 0 1 1 X+2 1 1 1 1 2 1 X 1 2 1 1 1 X 1 1 0 1 1 1 1 0 1 1 1 1 1 X+2 1 1 X+2 1 1 1 1 1 1 X+2 2 0 1 1 0 1 X 1 2 0 1 0 0 X 1 1 1 0 1 1 1 2 1 1 0 1 1 0 X+3 1 X+1 X+2 1 2 3 1 X X+3 1 1 1 X 1 1 X+2 1 0 X+1 1 X+2 1 2 X+1 1 3 1 1 1 1 2 X+2 1 X+1 X+1 1 X+2 X+3 3 X+1 1 1 0 1 2 X 1 X+3 2 1 2 X+1 2 2 0 0 1 1 1 X+3 X+1 1 2 X+2 2 1 1 1 1 1 1 X+1 3 3 1 X X+3 2 1 3 0 0 0 X 0 X+2 0 2 2 X X+2 0 X+2 X+2 2 0 X X+2 0 X+2 2 X+2 0 X X+2 X+2 0 2 X+2 2 X+2 0 X+2 X 2 X+2 2 X+2 0 0 0 0 X X+2 2 X X X X 0 0 X 2 X+2 2 2 X+2 2 X+2 0 X+2 X+2 0 2 X+2 0 0 2 X X 0 X+2 X 2 X 2 2 X+2 0 X+2 X X 0 0 0 X+2 0 0 0 0 X 0 0 0 2 2 2 2 0 2 X+2 X+2 X X+2 X+2 X X+2 X+2 X X+2 X+2 X+2 2 X 2 X+2 0 0 0 2 X+2 X X+2 X+2 X+2 X 0 2 2 X 0 0 X X+2 X X+2 2 X+2 0 0 2 0 0 0 X X+2 2 X X 2 0 X+2 X 0 X+2 2 2 X X+2 0 0 X+2 0 2 X X X+2 0 0 2 X X+2 0 0 0 0 0 2 0 0 0 2 2 0 2 2 0 0 2 2 0 2 0 2 0 2 0 0 2 2 0 2 0 2 0 0 2 0 2 0 2 2 2 2 2 2 2 2 2 0 0 0 2 0 2 0 2 0 0 2 2 2 0 0 2 2 2 2 0 2 0 0 0 0 0 0 2 0 0 0 0 2 0 0 0 2 2 2 0 0 0 0 0 0 2 2 2 0 2 0 2 0 0 2 2 0 2 0 2 2 0 0 0 0 2 0 2 2 0 0 2 2 2 2 0 0 0 2 0 2 0 0 2 2 2 0 0 0 0 2 0 2 2 0 0 2 2 2 0 2 2 0 2 0 2 0 2 2 0 2 0 0 2 2 2 2 2 2 2 0 2 2 2 2 0 generates a code of length 86 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 78. Homogenous weight enumerator: w(x)=1x^0+75x^78+140x^79+236x^80+246x^81+275x^82+340x^83+367x^84+314x^85+259x^86+376x^87+315x^88+248x^89+203x^90+246x^91+195x^92+76x^93+67x^94+38x^95+16x^96+10x^97+5x^98+6x^99+17x^100+2x^101+8x^102+6x^103+4x^104+3x^110+1x^114+1x^116 The gray image is a code over GF(2) with n=344, k=12 and d=156. This code was found by Heurico 1.16 in 1.61 seconds.