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 X 1 1 1 X 1 1 1 1 0 X 1 X 1 1 1 1 1 2 1 X 1 1 X 1 1 1 X X X 1 0 X 1 1 1 1 2 1 1 1 X X 0 X 0 0 0 X X+2 X 0 2 2 0 X X+2 X X 0 X+2 2 X 0 X 0 2 X+2 X+2 2 X 0 0 X+2 X+2 2 X+2 X+2 X+2 2 X+2 X+2 X+2 X X+2 X+2 0 X X 0 X+2 X 2 2 0 X+2 X X 2 X+2 X+2 X 0 X X+2 X 0 2 0 2 X X X 2 X+2 2 X 0 0 0 2 0 0 X 0 X X X+2 0 0 0 X+2 X+2 X X 2 2 0 2 2 X X X 2 X+2 2 0 0 0 X X+2 X X+2 2 X 0 0 2 0 0 2 X+2 2 X+2 X X+2 2 X+2 X X 0 0 0 X 0 X 0 0 X 2 2 X 2 0 X X X+2 X 0 2 X X 0 X 0 X+2 X+2 X+2 X+2 0 0 0 X X 0 X+2 X 2 X+2 X 2 2 X X 2 2 X+2 X+2 X X 2 X+2 0 2 2 2 X 0 X+2 2 X X+2 X 0 0 X X+2 2 0 X+2 0 2 0 X+2 X+2 X X 0 X 0 2 0 X+2 2 X X X X 0 2 X+2 X X+2 X X X+2 2 X X 0 X 2 2 0 2 2 X+2 0 0 0 0 2 0 0 0 2 0 0 0 0 0 0 0 2 2 2 2 0 0 2 0 2 2 0 2 0 2 0 2 0 2 2 2 0 0 2 2 0 0 2 2 2 2 0 0 2 2 0 2 0 0 2 2 2 2 2 2 2 2 2 2 2 0 2 0 2 2 2 0 2 2 0 2 2 0 0 0 0 0 0 2 0 2 0 0 2 2 0 2 2 2 2 2 0 0 0 0 0 0 2 0 2 2 2 2 2 2 2 0 2 0 2 0 0 0 2 0 0 0 0 0 2 0 2 2 2 0 2 0 0 2 0 2 2 2 2 0 2 0 0 0 2 2 2 2 0 0 0 0 0 0 2 2 0 0 0 0 0 0 2 2 2 2 0 0 2 0 0 0 2 0 0 0 2 0 2 2 2 2 0 2 2 2 2 2 0 2 0 0 2 0 0 0 2 2 2 2 0 0 2 0 0 2 2 0 0 2 0 0 2 0 2 0 2 0 0 0 2 0 2 2 0 0 0 0 0 0 2 2 2 0 generates a code of length 78 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 69. Homogenous weight enumerator: w(x)=1x^0+74x^69+109x^70+136x^71+164x^72+202x^73+217x^74+316x^75+323x^76+350x^77+464x^78+342x^79+367x^80+286x^81+148x^82+90x^83+106x^84+120x^85+67x^86+54x^87+50x^88+48x^89+19x^90+18x^91+10x^92+8x^93+4x^95+2x^96+1x^124 The gray image is a code over GF(2) with n=312, k=12 and d=138. This code was found by Heurico 1.16 in 25.1 seconds.