The generator matrix 1 0 1 1 1 X+2 1 1 0 1 1 X+2 1 X+2 1 1 0 1 1 0 1 1 1 X+2 1 0 1 1 1 X+2 1 X+2 1 1 0 0 X+2 1 1 1 X+2 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 X+2 X 2 1 1 X 1 0 1 X+1 X+2 1 1 0 X+1 1 X+2 3 1 X+2 1 X+1 0 1 3 0 1 X+1 X+2 3 1 0 1 X+1 3 X+2 1 3 1 X+2 3 1 1 1 X+1 0 X+1 1 3 2 X+2 1 X+1 X+2 X+1 1 X+3 3 X 0 1 3 0 X 1 1 1 0 3 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 2 0 2 2 2 0 0 2 0 2 2 0 2 2 0 2 2 2 0 0 2 2 2 0 0 2 0 0 2 2 2 0 2 0 0 2 2 0 0 0 0 0 2 0 0 2 2 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 2 2 0 2 2 2 0 2 2 0 2 2 0 0 0 2 2 2 2 0 2 0 0 0 0 2 2 2 0 2 0 2 0 2 2 2 0 0 0 2 2 0 0 0 2 2 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 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 2 2 2 2 2 2 2 0 2 2 2 0 2 2 0 2 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 2 2 0 2 2 0 2 2 2 0 2 2 0 2 0 0 0 2 0 2 2 0 2 2 2 0 2 0 0 2 0 2 2 0 0 0 2 0 0 2 0 0 2 2 2 2 0 0 0 0 0 0 0 0 0 2 0 0 0 2 0 2 0 2 2 0 0 2 2 0 0 2 2 2 0 2 0 0 0 2 0 0 0 0 2 2 2 0 0 2 2 2 2 0 2 2 0 2 2 0 0 0 2 2 2 2 0 2 0 2 0 2 0 0 0 0 0 0 0 0 2 0 0 0 2 0 2 2 0 0 0 2 2 2 2 0 2 0 0 2 2 2 2 0 0 0 0 0 0 2 0 2 0 2 2 2 2 2 0 0 0 2 2 0 2 0 0 2 0 0 0 0 2 0 2 0 0 0 0 0 0 0 0 0 0 2 0 2 2 0 2 2 0 0 2 0 0 2 0 0 2 2 2 0 0 2 2 0 2 0 2 0 2 2 0 0 2 0 2 2 0 0 2 0 2 0 0 2 0 2 2 0 2 2 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 2 0 2 2 0 0 2 0 2 2 0 0 0 2 2 2 0 2 2 2 2 0 0 0 0 0 0 0 0 2 2 2 0 0 0 2 2 0 0 2 2 2 0 0 0 2 2 0 0 0 2 0 generates a code of length 64 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 52. Homogenous weight enumerator: w(x)=1x^0+77x^52+20x^53+81x^54+80x^55+317x^56+190x^57+655x^58+362x^59+1509x^60+624x^61+2313x^62+792x^63+2480x^64+756x^65+2293x^66+604x^67+1451x^68+364x^69+637x^70+200x^71+263x^72+94x^73+105x^74+10x^75+31x^76+39x^78+11x^80+19x^82+4x^84+2x^86 The gray image is a code over GF(2) with n=256, k=14 and d=104. This code was found by Heurico 1.16 in 14.5 seconds.