The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 0 1 X 0 1 1 X X 2 0 1 1 0 1 1 0 1 0 X 2 1 X 0 1 X 1 X 1 1 0 1 X X X 1 X 1 0 X 0 X 0 0 X X+2 0 2 X 0 X+2 2 X+2 X X+2 0 X 0 X 2 0 X 0 2 X+2 X 0 X+2 X 2 X 0 X X 2 0 X+2 0 0 X 2 X 0 X+2 X X X X X 2 0 X 2 X 2 2 2 X+2 2 X+2 0 X+2 0 0 X X 0 X+2 X 0 0 X X 2 2 X+2 X 2 0 0 X 0 X X X+2 0 2 X 0 0 X+2 0 0 X+2 2 X+2 X X X 2 X X X 0 X X X 0 0 0 X 2 X X X 2 X+2 X+2 X 0 X 0 X 0 2 X+2 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 2 0 2 2 2 0 2 2 2 0 2 2 2 0 0 0 2 0 0 2 2 0 0 2 2 2 0 2 0 0 2 2 0 0 2 0 2 2 0 2 0 0 0 2 2 2 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 2 2 0 2 0 2 2 2 2 2 2 0 2 0 2 0 2 0 0 2 0 0 0 2 2 2 2 2 2 0 0 0 0 2 0 0 2 2 0 0 2 0 0 2 2 0 0 2 0 0 0 0 0 2 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 2 2 2 0 2 2 2 2 0 0 2 0 2 2 2 0 2 2 0 0 2 0 0 0 0 0 0 2 2 2 2 0 2 0 2 2 2 0 2 2 0 2 2 0 0 0 0 0 0 2 0 0 0 2 0 0 0 0 0 2 2 2 2 2 2 0 0 2 2 2 0 0 0 0 2 2 2 0 2 0 2 2 2 0 0 0 2 0 2 2 2 2 0 0 2 2 2 2 0 2 0 2 2 0 0 2 2 0 0 0 0 0 0 0 2 0 2 2 2 2 0 0 0 2 0 0 2 2 0 2 0 0 0 0 2 0 2 0 2 2 0 0 0 2 2 0 0 2 2 2 0 0 2 0 2 2 0 2 0 0 2 0 2 2 2 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 2 2 2 2 2 0 2 2 0 0 0 2 0 2 2 0 0 2 0 2 0 2 2 2 2 0 2 2 2 2 0 0 2 0 2 0 0 2 2 0 2 2 0 2 0 0 2 2 2 0 0 2 generates a code of length 64 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 53. Homogenous weight enumerator: w(x)=1x^0+46x^53+82x^54+90x^55+200x^56+184x^57+420x^58+244x^59+696x^60+220x^61+1052x^62+284x^63+1203x^64+232x^65+1152x^66+184x^67+765x^68+232x^69+280x^70+178x^71+169x^72+96x^73+72x^74+36x^75+22x^76+12x^77+8x^78+8x^79+10x^80+4x^82+5x^84+2x^85+2x^86+1x^88 The gray image is a code over GF(2) with n=256, k=13 and d=106. This code was found by Heurico 1.16 in 8.59 seconds.