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 2 X 0 X 1 2 1 X X 1 X 2 2 1 0 1 1 2 1 1 1 0 1 1 0 1 1 2 1 2 1 1 1 1 1 X 1 2 1 2 X X 1 1 1 1 1 0 1 0 X 0 0 0 0 0 0 2 2 X X+2 X 0 0 2 X+2 X+2 X X X X 0 X X+2 X 0 X X+2 2 X+2 2 2 X+2 X 0 0 X 2 X X 0 X+2 X 2 X+2 2 X+2 X 0 0 X 2 X X+2 X X X+2 X+2 2 X X+2 0 X X+2 0 2 X+2 X X X+2 X X 2 2 0 2 2 X 2 2 X 2 X+2 0 2 0 0 0 0 X 0 0 0 0 0 0 0 0 0 2 X+2 X+2 X+2 X X+2 X+2 X 2 2 X+2 X+2 0 0 X X X X+2 X+2 X+2 2 2 X+2 X X 2 2 X+2 0 2 X 0 X 2 0 2 X X 2 X+2 2 X+2 X+2 0 X+2 X+2 0 0 2 2 2 2 X 0 X 2 0 2 X+2 X+2 X+2 0 0 0 0 X+2 X+2 X+2 X+2 0 0 0 X X 0 2 0 0 0 X 0 0 2 X+2 X X X X 2 X+2 X 2 2 0 2 2 2 2 2 X X+2 X 2 X X+2 X+2 X X+2 0 2 0 0 0 X+2 X+2 X X+2 X X+2 2 2 2 X X 0 X 0 X X+2 0 X+2 2 X+2 0 X 2 X X X 0 X 2 0 0 2 2 X 0 2 2 X+2 X+2 X X 2 X+2 X 2 X X+2 X 0 2 2 0 0 0 0 X 0 X+2 X+2 X 2 X+2 X+2 0 X X 0 2 X 0 X+2 X+2 X X+2 X 2 2 X 2 2 0 X+2 2 0 X+2 X X+2 2 0 X+2 X+2 X X+2 X+2 2 2 X+2 2 0 0 0 0 0 0 2 2 2 0 X+2 X X X 0 X X+2 2 0 X+2 X X+2 X+2 X 0 2 X+2 0 X X X+2 X X X 2 X+2 X X 0 X 2 0 0 0 0 0 X X 2 X+2 X X+2 2 X X 0 X 0 X+2 X+2 0 X 2 2 X+2 2 X X+2 X+2 2 X 2 2 X+2 0 X X+2 0 0 0 0 X X X+2 0 X+2 X+2 0 2 X+2 0 X X 0 0 2 X+2 2 0 X+2 X+2 2 0 0 X+2 X+2 X 2 X+2 2 0 X+2 2 X+2 X X+2 0 2 0 X+2 0 X 2 2 2 2 2 0 X+2 generates a code of length 88 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 77. Homogenous weight enumerator: w(x)=1x^0+50x^77+155x^78+146x^79+207x^80+288x^81+323x^82+406x^83+456x^84+542x^85+599x^86+712x^87+702x^88+588x^89+586x^90+606x^91+449x^92+294x^93+253x^94+206x^95+147x^96+110x^97+113x^98+70x^99+44x^100+32x^101+45x^102+24x^103+7x^104+14x^105+6x^106+6x^107+2x^108+2x^109+1x^132 The gray image is a code over GF(2) with n=352, k=13 and d=154. This code was found by Heurico 1.16 in 8.3 seconds.