The generator matrix 1 0 0 0 1 1 1 0 1 1 1 1 2 2 0 1 0 0 2 2 1 0 2 1 1 1 2 1 0 1 1 1 2 2 1 1 1 0 1 1 1 2 0 0 1 1 1 1 2 2 0 2 2 2 2 1 0 1 0 0 0 1 1 1 0 0 3 3 1 2 1 3 1 0 2 0 0 1 1 0 3 2 1 1 1 3 0 3 1 1 0 3 0 0 2 1 1 2 2 2 0 2 0 1 2 2 1 1 1 0 1 0 0 0 1 0 1 1 0 1 0 1 1 2 0 1 3 2 1 1 1 0 0 0 3 2 3 3 1 3 3 1 3 0 0 2 1 0 0 1 2 1 2 1 1 1 0 0 1 0 0 1 3 1 0 2 0 3 0 0 0 1 1 0 1 1 1 0 1 2 1 3 0 2 1 3 0 1 1 0 1 2 0 1 0 1 2 1 2 3 3 3 2 2 1 2 2 0 3 1 2 2 3 0 2 1 1 3 3 3 2 1 3 2 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 2 2 2 2 2 2 2 0 2 0 2 2 2 0 2 2 0 0 2 0 2 0 2 2 0 0 2 2 2 0 2 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 2 0 2 0 0 2 2 0 0 2 0 0 2 2 0 2 2 2 2 2 0 0 2 2 0 2 0 2 0 0 0 0 0 2 2 0 2 2 0 2 2 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 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 2 2 2 0 2 2 2 0 0 0 0 0 0 0 0 2 0 0 2 2 0 0 2 0 2 2 2 2 0 2 0 0 2 0 2 2 2 0 2 2 0 0 0 0 0 0 0 2 0 0 2 2 2 2 0 2 2 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 2 0 2 0 0 0 0 0 2 2 0 2 2 2 0 2 0 0 2 0 2 2 0 2 2 0 2 0 2 2 0 0 0 2 2 2 0 2 0 2 2 2 2 2 2 2 0 2 0 0 0 0 0 0 0 0 0 2 0 2 2 2 2 2 2 0 0 2 0 2 0 2 0 2 2 0 2 0 2 2 2 2 0 2 0 2 0 0 0 0 0 0 2 0 2 2 2 0 0 0 2 2 0 2 generates a code of length 56 over Z4 who´s minimum homogenous weight is 44. Homogenous weight enumerator: w(x)=1x^0+217x^44+458x^46+1030x^48+1256x^50+1890x^52+2064x^54+2363x^56+2224x^58+2073x^60+1290x^62+905x^64+344x^66+181x^68+44x^70+36x^72+6x^76+1x^84+1x^88 The gray image is a code over GF(2) with n=112, k=14 and d=44. This code was found by Heurico 1.16 in 57.4 seconds.