The generator matrix 1 0 1 1 1 X+2 1 1 2 1 X 1 1 1 0 1 1 X+2 1 X 1 1 2 1 1 1 X+2 1 1 1 X 1 X X+2 1 X+2 1 1 1 X+2 1 1 1 2 X 1 X 1 1 X 1 2 1 X 2 1 1 1 1 1 1 1 1 1 1 1 X X+2 0 2 2 2 X 2 1 2 1 1 0 1 1 0 X+3 1 X X+3 1 3 1 0 2 X+1 1 1 X+2 1 3 1 X X+1 1 X+2 X+2 3 1 X 2 3 1 X+1 1 1 1 1 1 X+2 X+3 1 2 X+3 X+2 1 1 X 1 X+1 2 1 X+2 1 1 1 1 3 2 2 1 X+3 X+2 X X+3 X+1 X+2 1 0 1 1 1 1 1 1 2 X+3 1 3 2 0 0 X 0 X+2 0 0 2 2 0 2 X X+2 X+2 X X+2 X X 0 X 2 0 X+2 2 X X+2 2 0 X+2 0 X+2 2 X+2 2 2 0 X X 0 X+2 X+2 0 2 X+2 2 2 X+2 X 0 2 0 0 X X 2 X X+2 X+2 0 0 X+2 2 2 X X X+2 0 2 X 0 0 0 0 X X+2 2 X 2 0 0 0 X 0 0 X X+2 X+2 2 X X 0 X X X+2 X+2 2 X+2 X 0 0 2 2 0 X+2 2 X 2 0 2 0 X+2 0 X+2 X+2 X+2 X+2 X 2 0 2 2 X+2 X X 0 2 0 X 0 0 0 2 X+2 X+2 X X+2 0 X 0 X+2 0 2 0 X X+2 X X 2 X+2 2 0 0 2 2 0 X+2 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 2 0 2 2 2 0 2 0 2 2 2 2 2 0 0 2 0 2 2 0 0 0 0 0 2 2 2 2 2 2 0 0 0 2 0 0 2 2 2 2 0 2 0 0 2 2 2 2 2 0 0 2 2 0 0 2 2 2 0 0 0 2 2 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 0 2 2 0 2 2 2 2 0 2 0 2 2 0 0 0 2 0 2 2 2 2 0 0 2 2 0 0 0 0 0 0 2 0 0 0 2 0 0 2 0 0 2 2 2 2 2 0 2 0 0 2 0 0 2 2 0 0 2 2 0 0 2 0 2 0 0 2 0 0 0 2 2 0 2 2 0 2 2 2 2 0 0 2 2 0 2 0 2 0 2 0 0 2 0 2 2 2 2 0 0 0 2 2 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+62x^69+138x^70+340x^71+241x^72+576x^73+449x^74+778x^75+495x^76+890x^77+555x^78+834x^79+454x^80+686x^81+372x^82+516x^83+162x^84+306x^85+113x^86+72x^87+37x^88+28x^89+26x^90+18x^91+15x^92+6x^93+9x^94+2x^95+3x^96+6x^97+1x^102+1x^106 The gray image is a code over GF(2) with n=312, k=13 and d=138. This code was found by Heurico 1.16 in 5.77 seconds.