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 1 1 1 1 1 1 1 X 0 X 0 X X 2 X 0 1 X 0 1 X X X 1 X 1 2 1 X X 1 X 2 1 2 1 2 1 1 2 X X X 1 0 X 0 0 0 0 0 0 0 0 2 X X X+2 0 X+2 X+2 0 2 X X+2 2 X X X 2 X 0 X 2 X+2 X X+2 0 2 0 2 2 X X+2 X X 2 0 0 X+2 2 0 2 0 X X 2 0 X+2 2 X+2 X+2 2 0 0 X+2 X+2 2 X 0 X 0 0 X+2 0 0 X 2 2 X X X 2 2 0 0 X 0 0 0 X 0 0 0 0 0 0 0 X+2 2 X X X X 0 X X 0 X+2 2 0 X+2 X X X+2 X+2 2 0 X+2 0 2 X 0 X+2 X 2 0 2 X+2 X X+2 X 0 X X X+2 X 2 X 0 2 X X 0 2 2 0 2 2 0 X+2 0 X+2 2 2 X+2 X X 0 2 2 0 X X+2 0 X 0 0 X+2 X 2 X+2 0 0 0 X 0 0 0 X X+2 X X X+2 0 X 2 0 X+2 X+2 2 X+2 X+2 X 0 2 0 2 X X X 2 X 0 2 X 2 2 X 2 X 2 X 2 0 0 X+2 X 0 2 2 X 0 X+2 X 2 2 0 X+2 2 X 2 0 2 X+2 X X+2 0 2 X X+2 X 2 X X+2 X+2 X 0 2 X+2 X 2 X X+2 X 2 0 0 0 0 X 0 X X X 2 X X X 2 2 X+2 X+2 2 X+2 2 X+2 X X+2 2 2 X 0 X+2 2 X+2 X+2 X X X X+2 X 2 0 0 0 X X X 0 2 0 0 X 2 2 X 2 2 X+2 0 X X 2 X 2 2 X+2 X+2 2 0 0 2 X+2 X+2 X+2 X+2 X+2 X 0 X 0 0 2 X+2 X X+2 X 2 0 0 0 0 0 0 X X 2 X+2 X+2 X X X+2 0 X 2 2 2 X X+2 0 2 2 0 X 0 X 2 2 X+2 X+2 X+2 X+2 X+2 2 X+2 2 2 X+2 X+2 X+2 X+2 2 0 X 0 X X 0 0 0 2 X X+2 2 0 X+2 X X X+2 X+2 X+2 0 X+2 X+2 0 2 0 X+2 0 X X+2 X+2 X 0 X 0 X+2 X X 0 X+2 2 X 0 0 0 0 0 0 2 2 2 2 2 2 2 0 2 0 0 0 2 2 0 0 0 0 2 2 0 2 2 0 0 0 2 0 2 0 2 2 0 2 2 0 0 2 0 2 2 0 2 0 2 0 0 2 0 2 0 0 2 2 0 0 2 2 2 0 0 0 0 0 0 2 0 2 0 2 2 2 2 0 2 2 2 2 generates a code of length 84 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 72. Homogenous weight enumerator: w(x)=1x^0+170x^72+506x^74+44x^75+738x^76+152x^77+1050x^78+300x^79+1247x^80+680x^81+1588x^82+876x^83+1791x^84+856x^85+1650x^86+692x^87+1296x^88+320x^89+882x^90+136x^91+596x^92+32x^93+394x^94+204x^96+8x^97+120x^98+34x^100+18x^102+2x^104+1x^116 The gray image is a code over GF(2) with n=336, k=14 and d=144. This code was found by Heurico 1.16 in 28.7 seconds.