The generator matrix 1 0 1 1 1 X+2 1 1 0 X+2 1 1 1 1 X 1 2 1 X+2 1 1 X+2 1 1 1 1 X 1 2 1 1 X 1 2 1 X+2 1 1 1 1 1 X 1 0 1 1 0 1 1 2 1 1 0 1 0 X+2 X 1 1 1 1 X+2 2 X X 1 2 1 2 1 X 1 2 1 1 1 0 1 1 0 X 2 X 1 0 1 1 0 1 1 X X+3 1 1 X+3 2 X X+1 1 X 1 1 1 3 0 1 X+3 X 2 0 1 X+3 1 X+1 X+3 1 X+2 1 X 1 3 3 X+3 X+2 X+2 1 X+1 1 3 X 1 3 3 1 0 0 1 X+3 1 1 1 X X+2 X+1 1 1 1 1 1 0 2 X+2 1 X+3 1 0 1 X+1 1 X 1 X X+1 X 1 X 0 X+1 0 0 X 0 0 0 0 0 0 2 X+2 X X+2 2 0 X X X X+2 2 X+2 X+2 X X X 0 X+2 X 2 2 X X+2 X X+2 2 X X 0 2 2 2 0 2 0 2 X 0 2 X+2 X+2 X 0 X 0 X 0 X X+2 0 X+2 X+2 0 X X+2 X+2 2 0 2 X+2 0 0 X 2 X+2 2 X+2 2 0 X+2 X X X+2 X+2 X+2 0 0 0 X 0 0 X 2 X X+2 0 X+2 X X 0 0 2 X X+2 X+2 2 0 X 2 X+2 X X+2 X+2 X+2 2 2 0 X X+2 2 0 0 2 2 0 X+2 X+2 X+2 X X+2 0 0 2 X 2 X+2 0 X+2 2 0 0 2 2 0 2 X+2 0 X 0 X+2 0 X X X X+2 2 X+2 X X X 0 2 X 2 X+2 0 X+2 X+2 X+2 0 0 0 0 X 0 0 X+2 X+2 X+2 2 X X X+2 X X+2 0 0 0 X X+2 0 2 2 2 X X X+2 0 0 X+2 X+2 2 0 X+2 X X+2 X X 2 X+2 2 X+2 2 0 X X 2 0 0 X X X+2 0 X+2 0 X+2 X 2 X+2 X+2 X+2 X X X+2 0 X X X X X+2 2 X X+2 0 2 0 2 X+2 0 X+2 X X 0 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 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 0 2 2 2 2 2 2 2 2 0 2 2 0 2 2 2 0 0 0 2 0 2 2 0 0 2 0 0 2 0 0 0 0 0 0 2 2 2 0 2 0 2 2 2 2 2 0 2 0 0 0 2 0 2 0 2 2 0 0 0 2 0 0 0 0 0 0 2 2 2 0 0 2 0 0 2 2 2 2 2 2 0 0 0 2 2 2 0 2 2 0 0 0 0 0 0 2 2 2 0 0 2 0 2 2 2 2 2 0 0 0 0 0 generates a code of length 84 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 74. Homogenous weight enumerator: w(x)=1x^0+251x^74+76x^75+570x^76+304x^77+865x^78+612x^79+1253x^80+964x^81+1448x^82+1136x^83+1668x^84+1108x^85+1532x^86+984x^87+1069x^88+596x^89+730x^90+244x^91+394x^92+92x^93+238x^94+20x^95+130x^96+8x^97+45x^98+27x^100+9x^102+6x^104+2x^106+1x^108+1x^112 The gray image is a code over GF(2) with n=336, k=14 and d=148. This code was found by Heurico 1.16 in 39.7 seconds.