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 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 2 2 X X X 2 X X 2 2 1 2 1 0 1 1 X 2 1 X X 1 1 0 1 1 X X X 0 X 0 0 0 0 0 0 0 0 2 X X X+2 0 X+2 X+2 0 X 2 X+2 2 X X X 2 X 0 X 2 X+2 X X+2 0 2 0 2 2 X X+2 X X 2 X X 2 0 X+2 2 X 2 X+2 X X 0 X X+2 2 X+2 0 0 0 2 0 2 X+2 2 X X X+2 X+2 2 X 0 0 X 0 0 0 0 0 0 0 X+2 2 X X X X 0 X 0 X X+2 2 0 X+2 X X X+2 X+2 2 0 X+2 0 2 X 0 X+2 X 2 0 2 X+2 X X+2 X+2 0 2 2 2 X 2 X+2 2 2 2 X+2 0 2 X 0 2 2 X 2 X+2 X+2 X 2 2 0 2 X X+2 2 0 0 0 X 0 0 0 X X+2 X X X+2 0 X 2 0 X+2 X+2 X+2 2 X+2 X 0 2 0 2 X X X 2 X 0 2 X 2 2 X 2 X 2 X 2 0 0 2 0 X 2 0 0 2 X+2 X X+2 X X+2 0 0 X+2 X 0 X X+2 X X X 2 2 X+2 2 0 2 2 0 0 0 0 X 0 X X X 2 X X X 2 2 X+2 X+2 2 2 X+2 X+2 X X+2 2 2 X 0 X+2 2 X+2 X+2 X X X X+2 X 2 0 0 0 X X X 0 X+2 X X X+2 0 2 2 X 0 0 2 X+2 2 X 0 0 X+2 X+2 X+2 X X+2 2 X X+2 X+2 X+2 X+2 X X 0 0 0 0 0 X X 2 X+2 X+2 X X X+2 0 X 2 2 2 X+2 X 0 2 2 0 X 0 X 2 2 X+2 X+2 X+2 X+2 X+2 2 X+2 2 2 X+2 X+2 X+2 X+2 2 2 2 X X+2 X+2 0 X+2 X+2 2 0 X+2 X 2 X+2 0 2 2 2 2 2 0 X X+2 X+2 0 0 X 2 0 2 0 0 0 0 0 0 2 2 2 2 2 2 2 0 2 0 0 0 2 2 0 0 0 0 2 2 0 2 2 0 0 0 2 0 2 0 2 2 0 2 2 0 0 2 2 0 2 0 2 2 2 0 0 2 0 2 2 2 0 0 0 2 2 0 0 2 2 2 2 2 2 2 0 generates a code of length 73 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 62. Homogenous weight enumerator: w(x)=1x^0+214x^62+8x^63+589x^64+64x^65+862x^66+208x^67+1079x^68+512x^69+1553x^70+772x^71+1860x^72+932x^73+1995x^74+844x^75+1504x^76+476x^77+1120x^78+212x^79+684x^80+60x^81+404x^82+4x^83+263x^84+4x^85+105x^86+33x^88+19x^90+2x^92+1x^104 The gray image is a code over GF(2) with n=292, k=14 and d=124. This code was found by Heurico 1.16 in 34.2 seconds.