The generator matrix 1 0 1 1 1 X+2 1 1 2 1 X 1 1 1 X 1 1 2 1 1 0 1 1 X X+2 1 1 1 0 X 1 1 2 1 X 1 1 X+2 2 1 1 1 0 1 X 1 1 1 1 1 X 1 1 1 1 1 X+2 X X+2 1 0 1 1 1 1 2 1 2 1 1 2 1 1 1 1 1 1 0 1 1 X+2 X+3 1 0 X+1 1 X 1 3 X X+3 1 2 1 1 0 1 1 X+2 X+1 1 1 1 X X+3 1 1 0 3 1 3 1 X X+1 1 1 2 X+1 0 1 1 1 2 X+2 X+1 X+1 X 1 X+1 2 3 X+2 0 1 2 1 X+3 1 X+2 X+3 X+2 2 1 X+3 X X+2 0 1 3 0 X+2 X+2 X+1 X+1 0 0 X 0 X+2 0 X+2 2 X X X 2 X+2 X X+2 X+2 X X 0 0 2 0 2 X 0 X+2 2 X+2 2 0 2 2 X+2 2 X+2 X 2 X+2 2 X X+2 2 X+2 X+2 2 X 2 2 X 0 0 X 0 X+2 X+2 X+2 0 X X+2 0 X+2 0 2 2 0 0 X X X+2 0 0 X+2 X 0 0 0 0 0 0 0 2 0 0 0 2 2 0 2 0 0 0 2 0 0 2 0 0 0 0 0 2 2 2 0 2 2 2 2 2 2 0 0 0 0 0 0 2 0 0 2 2 2 0 2 0 2 2 0 0 0 2 0 2 2 2 0 2 0 2 2 0 2 2 2 2 2 0 0 2 0 0 2 0 0 0 0 0 0 2 0 0 0 0 2 0 0 0 2 2 2 0 2 2 0 2 2 2 2 0 2 0 2 2 2 2 0 0 2 0 0 0 2 2 2 2 0 2 0 2 2 0 2 0 0 2 0 0 0 0 0 2 2 0 0 2 2 0 2 0 0 2 0 2 0 2 2 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 0 0 2 2 2 0 2 0 0 2 2 2 0 2 2 2 0 2 2 0 0 2 2 2 0 2 2 0 2 2 2 2 2 0 0 2 0 2 2 2 0 0 2 0 0 0 2 2 2 0 2 0 2 0 2 2 0 0 2 0 0 0 0 0 0 0 2 0 2 0 0 0 0 2 2 2 2 0 0 2 2 2 2 2 2 0 2 0 0 0 2 2 0 0 0 2 0 0 0 2 2 2 0 2 2 0 0 2 0 2 2 2 0 2 0 0 0 2 0 2 2 0 2 0 0 0 2 2 0 2 0 2 0 0 2 0 2 generates a code of length 77 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 69. Homogenous weight enumerator: w(x)=1x^0+46x^69+102x^70+196x^71+279x^72+336x^73+332x^74+330x^75+344x^76+322x^77+346x^78+336x^79+265x^80+256x^81+226x^82+124x^83+115x^84+44x^85+16x^86+16x^87+12x^88+14x^89+2x^90+18x^91+4x^92+4x^93+4x^95+2x^96+2x^97+1x^100+1x^104 The gray image is a code over GF(2) with n=308, k=12 and d=138. This code was found by Heurico 1.16 in 1.38 seconds.