The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 0 1 1 1 1 X 0 1 X 0 X 0 1 1 1 X 0 1 0 1 1 1 0 0 1 1 1 X 1 1 X 0 X 1 1 0 X 0 X+2 0 X+2 0 X+2 0 X+2 2 X+2 0 X+2 0 X+2 X 2 X+2 X 0 X+2 0 X+2 X+2 X 0 X+2 X X+2 X 0 X+2 X X+2 X X X 2 X+2 2 X X 2 X X+2 X+2 X+2 X+2 2 X X+2 0 0 0 0 2 0 0 0 0 0 0 0 2 0 2 0 0 0 0 2 0 0 2 2 0 2 2 2 2 0 0 2 0 0 2 0 0 2 0 2 0 2 0 2 0 2 0 0 2 2 2 2 0 2 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 0 0 2 0 0 2 2 2 2 2 2 0 0 2 2 0 2 0 0 2 0 2 2 0 2 0 2 2 0 0 2 0 2 0 2 0 0 2 2 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 2 0 0 2 2 2 0 0 2 0 2 2 0 0 2 2 2 2 0 0 2 0 2 2 2 2 2 2 0 0 2 0 0 2 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 2 0 0 2 0 2 0 2 2 2 2 0 0 2 0 2 2 2 0 0 0 2 2 0 2 0 2 0 2 0 2 0 2 2 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 2 0 2 0 0 0 0 0 0 2 0 0 0 2 2 2 0 2 2 2 0 0 2 2 2 2 2 0 2 2 0 0 2 0 0 2 2 0 0 2 2 0 0 0 0 0 0 0 0 2 0 0 0 2 0 0 2 2 0 2 2 2 0 2 2 2 2 0 0 2 2 2 0 0 2 2 0 0 0 2 0 0 2 0 0 0 2 0 2 2 0 2 0 2 0 2 0 0 0 0 0 0 0 0 2 0 2 0 2 0 2 2 2 0 0 2 2 2 2 0 0 2 0 0 0 2 0 0 2 2 2 0 2 0 2 0 2 0 2 0 2 2 0 0 2 0 2 2 0 2 0 0 0 0 0 0 0 0 0 2 0 2 0 0 2 0 2 2 2 2 0 2 2 0 2 2 2 0 0 2 2 0 0 0 2 0 0 2 0 2 0 0 2 2 2 0 0 0 2 0 0 0 0 0 generates a code of length 54 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 42. Homogenous weight enumerator: w(x)=1x^0+32x^42+6x^43+81x^44+60x^45+154x^46+160x^47+188x^48+454x^49+204x^50+980x^51+254x^52+1408x^53+257x^54+1416x^55+243x^56+964x^57+217x^58+470x^59+173x^60+180x^61+108x^62+40x^63+57x^64+6x^65+38x^66+20x^68+9x^70+7x^72+5x^74 The gray image is a code over GF(2) with n=216, k=13 and d=84. This code was found by Heurico 1.16 in 4.77 seconds.