The generator matrix 1 0 0 1 1 1 1 1 1 1 1 1 1 1 2a+2 1 2 1 1 1 0 1 0 1 1 1 1 1 2a+2 1 1 1 2a 1 2a 1 0 1 1 1 2a+2 1 1 1 2 1 1 1 1 1 1 1 1 1 2a+2 1 0 1 0 0 2 2a+2 1 3a+2 1 2a+3 3a 2a+3 3a+3 3a+1 1 a+1 1 a 3a+1 a 1 2a 1 3 2a+2 a+2 2a+2 2a+1 0 2 3a+2 1 2a+2 a+1 1 3a+2 1 2a+3 3a+1 a+1 1 2 a 0 1 3a 3a 2a a+3 a 2a+3 3 3a+1 a+1 1 a+3 0 0 1 1 3a+2 3a+3 3 2a+3 3a+3 a a+1 2 a+3 2a 3 3a+2 a+3 a 2a+3 0 3a+2 3a 2a+2 0 2a+3 2 a+3 2a+1 1 2a a+3 2 1 3a+3 a+1 2a+1 3a a+1 2a+1 2a+3 a+1 2a+2 a 2a+1 2a+3 a+1 2a+3 a+1 2a+2 3a+2 3a 2a+1 3a+1 a 2a 3a 0 0 0 2a+2 0 0 2a+2 2a+2 2a 2a 2a+2 0 0 0 0 2a 0 2 2 2a 2a+2 2 2 2a+2 2a 2a+2 2a+2 2a 2a 2a 2a 2 2 2 2 2 2a 2a+2 2a 2a+2 2a+2 2 0 2 2a+2 0 0 2a 2 2a+2 0 0 2a+2 2 2a+2 0 generates a code of length 56 over GR(16,4) who´s minimum homogenous weight is 157. Homogenous weight enumerator: w(x)=1x^0+528x^157+564x^158+336x^159+300x^160+1104x^161+1080x^162+552x^163+510x^164+1548x^165+1296x^166+456x^167+384x^168+1356x^169+948x^170+396x^171+201x^172+1380x^173+696x^174+348x^175+261x^176+756x^177+612x^178+156x^179+123x^180+240x^181+180x^182+60x^183+6x^184+3x^188+3x^196 The gray image is a code over GF(4) with n=224, k=7 and d=157. This code was found by Heurico 1.16 in 67.4 seconds.