The generator matrix 1 0 0 1 1 1 2X 1 1 0 1 1 2 3X 1 3X+2 1 2X X+2 1 1 1 X+2 3X+2 2X+2 1 1 1 X 1 1 1 1 1 1 1 3X 2X 2 1 1 2X+2 2X 1 X 1 X 3X+2 1 X+2 1 2 2X+2 1 0 1 0 2X 3 2X+3 1 X 3X 3X X+3 3X+3 1 1 0 1 X+3 1 2X+2 3X+1 3 2X 1 3X 1 2 3X+2 X+1 1 X 2X+1 3X+1 3X+2 1 3X X+2 1 X+2 1 X+2 3X+1 1 1 3X+3 1 0 X+2 0 3X+2 3X+2 2X+2 3X 2X+2 2X+3 0 0 1 3X+1 X+1 2X X+1 X 3 1 2X+3 3X X+2 2X+3 3X+2 0 X+3 2X+3 1 X+2 2X+3 1 3X+1 1 3X 2X+2 3X+3 2X 2X+2 0 X 2X+1 2X+2 3X+1 3X+3 3X+2 X+2 1 2 3 X+1 3 3X+3 2X+1 3X 3X+3 1 1 X 1 X+2 1 1 3X generates a code of length 54 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 51. Homogenous weight enumerator: w(x)=1x^0+612x^51+636x^52+900x^53+470x^54+496x^55+241x^56+332x^57+150x^58+152x^59+34x^60+64x^61+3x^62+4x^63+1x^70 The gray image is a code over GF(2) with n=432, k=12 and d=204. This code was found by Heurico 1.16 in 21.6 seconds.