The generator matrix 1 0 0 1 1 1 0 1 1 1 1 0 1 0 2 1 0 2 1 1 2 1 0 1 0 1 1 0 1 0 1 0 1 1 0 2 1 1 0 2 1 2 0 1 2 0 3 1 3 1 0 1 3 3 0 0 1 1 1 0 1 2 1 0 3 1 2 0 1 1 1 1 2 0 3 1 2 3 2 2 1 0 0 0 2 0 0 0 2 2 2 2 2 0 0 0 0 2 2 2 0 0 0 0 2 2 0 2 0 0 0 0 2 0 0 0 2 0 2 2 2 2 2 0 0 0 0 0 2 0 2 2 2 0 2 0 0 0 0 0 2 0 0 0 2 0 0 0 2 2 0 2 2 2 2 0 2 0 2 2 0 0 0 0 0 0 0 0 2 2 2 2 2 0 2 2 2 2 0 2 2 2 2 0 0 2 2 2 0 generates a code of length 27 over Z4 who´s minimum homogenous weight is 22. Homogenous weight enumerator: w(x)=1x^0+72x^22+174x^23+126x^24+68x^26+180x^27+64x^28+100x^30+144x^31+63x^32+12x^34+12x^35+4x^38+2x^39+2x^40 The gray image is a code over GF(2) with n=54, k=10 and d=22. This code was found by Heurico 1.16 in 17.9 seconds.