The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 X X 0 X X 1 0 1 2 X 1 1 1 1 X 1 X 1 1 1 X 1 X 1 X 1 X 1 1 2 1 0 1 1 1 0 1 1 2 X 1 X X 0 X 0 0 0 0 0 0 2 2 X X+2 X 0 0 2 X+2 X+2 X X X X 0 X X+2 X 0 X X+2 2 X+2 2 2 X+2 X 0 0 X 2 0 X 2 X 2 X X X+2 X X X X 0 X 2 X+2 0 X X+2 X 0 X+2 X+2 X+2 2 0 X X 0 2 2 X X 0 0 X+2 2 X X X 2 2 2 0 2 0 0 X 0 0 0 0 0 0 0 0 0 2 X+2 X+2 X+2 X X+2 X+2 X 2 2 X+2 X+2 0 0 X X X X+2 X+2 X+2 2 2 X+2 X X 2 2 X 2 2 X 0 0 X 0 X+2 2 X+2 0 2 0 X X X+2 2 X+2 0 X+2 X+2 2 X+2 2 2 0 X 2 X X 0 X 0 0 2 0 X+2 0 X 0 2 0 X 2 0 0 0 X 0 0 2 X+2 X X X X 2 X+2 X 2 2 0 2 2 2 2 2 X X+2 X 2 X X+2 X+2 X X+2 0 2 0 0 0 X+2 X+2 X X+2 X 2 X X X+2 X X+2 2 X 2 2 X+2 0 0 X+2 X X+2 2 X+2 X+2 0 2 2 X+2 X+2 2 X+2 X+2 2 X+2 X+2 X 2 X+2 0 2 X 0 X X+2 X+2 2 X 0 0 0 0 X 0 X+2 X+2 X 2 X+2 X+2 0 X X 0 2 X 0 X+2 X+2 X X+2 X 2 2 X 2 2 0 X+2 2 0 X+2 X X+2 2 0 X+2 X X+2 2 0 0 X X 0 0 2 0 0 2 X+2 0 X+2 X X 0 X 2 2 0 2 X 0 X X X 0 2 0 X 0 X+2 X X X+2 X X+2 0 2 X 2 X+2 0 0 0 0 0 X X 2 X+2 X X+2 2 X X 0 X 0 X+2 X+2 0 X 2 2 X+2 2 X X+2 X+2 2 X 2 2 X+2 0 X X+2 0 0 0 X X+2 X 2 2 0 0 X 2 X X X 2 0 X+2 0 0 2 0 X X 2 2 X X 2 X X 0 0 0 X X X+2 0 2 X+2 0 X+2 0 X 0 2 X 2 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+220x^74+8x^75+459x^76+48x^77+508x^78+152x^79+679x^80+372x^81+850x^82+516x^83+921x^84+384x^85+804x^86+288x^87+634x^88+212x^89+392x^90+60x^91+290x^92+8x^93+172x^94+118x^96+58x^98+31x^100+4x^102+2x^108+1x^124 The gray image is a code over GF(2) with n=336, k=13 and d=148. This code was found by Heurico 1.16 in 78.3 seconds.