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 2 X X 1 0 2 X 2 1 2 2 0 1 2 1 0 X 0 1 X 0 1 1 1 X 2 0 1 X 1 X 0 X 1 1 0 X 0 0 0 X X+2 X 0 2 2 X X+2 X X 0 0 0 2 X+2 X+2 2 X+2 X X+2 0 0 X+2 X 0 X 2 X 2 X X X 2 0 X 0 X 2 X 2 X 0 X X X 0 X X+2 2 2 0 X X+2 0 2 X 0 X+2 X+2 2 0 0 2 0 0 0 X 0 X X X+2 0 0 0 X X X 0 2 X+2 X 0 2 2 0 0 X+2 2 X X+2 2 X+2 0 X+2 X X+2 X X X X+2 0 2 X 2 X+2 X+2 0 X+2 X 2 2 2 X+2 X X+2 X X+2 X X 0 X 0 X+2 X X+2 X 2 X 0 0 2 X 0 0 0 0 X X 0 X+2 X 2 X 2 0 X 2 X+2 X 2 2 X X+2 2 X 0 X X+2 X+2 0 X+2 0 0 0 X+2 X+2 2 0 0 X+2 0 0 X+2 0 2 X 0 X+2 0 X X+2 2 0 2 X 0 2 X X 0 X 2 2 2 X+2 0 X X+2 X X X 0 0 0 0 0 2 0 0 0 2 2 2 2 2 0 0 2 2 0 2 2 0 2 2 0 0 0 0 2 2 2 2 2 0 0 0 0 2 0 2 0 2 0 0 0 0 2 2 2 0 2 0 2 0 2 2 2 2 0 0 0 2 0 2 2 0 0 2 2 0 0 0 0 0 0 2 0 0 0 2 0 2 2 2 0 0 2 2 2 2 0 0 0 2 0 0 0 0 2 2 0 0 2 2 0 0 2 2 2 2 0 2 2 2 0 2 0 0 0 0 0 2 2 0 2 2 0 0 2 0 2 0 2 2 0 0 2 0 0 0 0 0 0 0 0 2 0 2 0 0 2 2 2 0 0 2 0 2 2 2 0 2 0 0 0 2 0 0 0 2 2 0 2 2 2 2 0 2 2 0 2 0 0 2 0 2 2 0 0 0 0 0 2 0 2 0 2 0 2 0 2 2 0 2 2 2 2 0 0 0 0 0 0 0 0 2 0 0 2 0 0 0 0 2 0 0 0 2 2 2 2 2 2 2 0 2 2 0 0 2 2 0 2 0 0 2 2 0 2 2 0 2 2 2 0 0 0 0 0 2 2 0 2 2 0 0 0 0 2 0 0 2 0 2 0 2 0 generates a code of length 69 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 58. Homogenous weight enumerator: w(x)=1x^0+36x^58+78x^59+139x^60+232x^61+242x^62+308x^63+401x^64+506x^65+573x^66+620x^67+685x^68+686x^69+703x^70+638x^71+538x^72+392x^73+358x^74+322x^75+230x^76+184x^77+88x^78+60x^79+42x^80+46x^81+41x^82+20x^83+9x^84+2x^85+7x^86+2x^87+2x^88+1x^92 The gray image is a code over GF(2) with n=276, k=13 and d=116. This code was found by Heurico 1.16 in 6.09 seconds.