The generator matrix 1 0 1 1 1 X+2 1 1 2 1 1 X 1 1 0 X+2 1 1 0 1 1 X+2 1 1 1 X+2 1 1 0 1 1 1 0 X+2 1 1 X+2 1 1 0 1 1 1 2 0 1 1 1 X 1 X 1 1 1 0 1 1 0 2 2 1 X+2 1 1 1 1 1 0 X+2 1 1 1 1 1 X 1 X 0 1 1 X+2 X+3 1 0 X+1 1 X 3 1 0 X+1 1 1 2 X+2 1 3 X+2 1 X+3 1 X+3 1 1 2 1 X 2 3 1 1 X 3 1 X+3 0 1 1 X+1 X+1 1 1 X+1 X+3 1 1 0 1 X+2 X+3 1 1 X+3 X 1 1 1 X 1 X 0 X+2 X+3 X 1 1 X+1 X+3 X+1 2 2 0 1 0 0 0 X 0 X+2 0 X+2 0 X+2 X 2 X+2 0 2 0 X+2 X 2 X 2 X 2 X X 0 0 0 X 0 X+2 X 2 0 X+2 X+2 X 0 X+2 2 0 X+2 X+2 2 X+2 X 2 0 X+2 0 0 X+2 X 0 2 2 X+2 X 2 2 X+2 2 0 2 0 2 X 0 X+2 X 0 0 X 2 2 X 2 2 0 0 0 2 0 0 0 0 0 0 2 0 2 0 0 0 2 0 0 2 2 0 2 2 2 0 0 0 2 0 2 2 0 2 2 2 2 2 0 0 0 2 2 2 0 0 2 0 0 2 2 0 0 2 2 0 0 2 2 0 0 2 2 2 2 0 2 0 2 0 0 0 0 2 0 2 2 0 0 0 0 2 0 0 0 0 0 0 2 2 2 2 0 2 2 2 2 2 2 0 2 2 0 2 2 0 0 2 0 0 2 0 0 2 0 0 0 2 0 2 2 2 0 0 2 2 0 2 0 2 0 2 2 0 0 2 2 2 2 0 2 0 0 2 2 2 0 0 0 0 2 0 2 0 0 0 0 0 0 2 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 2 0 0 0 2 0 0 2 2 2 0 0 2 0 0 2 2 2 2 0 2 2 2 0 2 2 2 2 2 2 0 0 0 0 2 2 2 0 2 0 2 0 0 2 0 0 2 2 2 0 2 0 2 0 2 0 0 0 0 0 0 0 2 0 2 0 0 0 0 0 0 0 2 0 2 0 0 0 2 2 2 2 2 2 0 2 2 2 2 2 0 0 2 0 0 2 0 2 0 0 2 0 0 0 2 2 0 2 2 0 2 2 0 2 2 0 2 0 2 0 0 0 2 2 0 0 0 0 2 2 2 2 2 0 0 0 0 0 0 0 2 2 0 0 0 0 2 0 0 0 0 2 0 0 0 2 2 0 2 2 0 0 0 0 0 2 2 0 2 0 2 2 0 2 2 2 2 0 0 2 0 0 2 0 2 0 2 2 2 2 2 0 2 2 0 0 2 0 2 0 0 2 2 0 0 2 0 0 2 2 generates a code of length 77 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+144x^68+56x^69+272x^70+280x^71+670x^72+408x^73+746x^74+488x^75+786x^76+568x^77+836x^78+552x^79+727x^80+424x^81+454x^82+216x^83+268x^84+80x^85+90x^86+59x^88+24x^90+24x^92+10x^94+6x^96+2x^100+1x^104 The gray image is a code over GF(2) with n=308, k=13 and d=136. This code was found by Heurico 1.16 in 5.26 seconds.