The generator matrix 1 0 0 1 1 1 X 1 1 X+2 1 1 X X+2 X X 1 1 2 1 1 0 2 1 1 1 0 2 X 1 2 1 2 2 2 1 1 X+2 2 1 1 1 1 1 1 1 1 2 1 X 1 1 X 0 0 X X+2 1 1 0 1 1 1 1 1 X+2 1 1 X 1 X 1 0 X 1 2 0 1 1 0 1 0 X 1 X+3 1 X+2 0 2 1 X+1 1 1 X 1 1 X+2 1 0 X+3 1 1 0 X X+1 1 X X+2 1 1 2 1 1 1 3 X 1 X+2 0 2 2 X+1 X+2 0 0 1 X+2 X 1 X 1 1 1 1 2 1 X+3 1 0 X X+3 2 X+1 3 0 X+3 X X+2 X+2 1 X+3 X 1 X+3 X 1 X+1 2 0 0 1 1 X+3 X+2 1 X+3 X+2 1 1 0 X X+1 1 2 X 0 X+3 X+3 1 2 1 3 X+2 X+1 X+3 1 1 2 1 2 X+1 X X 2 3 2 1 3 X+1 2 X+3 1 X+3 2 1 1 X+2 X+3 2 2 X+2 X 2 1 2 X+2 X+2 1 3 X+1 3 X+3 X+3 1 X+1 X+2 1 X+3 X+1 X+2 1 0 X+2 1 2 X+2 X 0 0 0 2 0 0 0 0 2 2 0 0 2 2 2 2 2 2 2 0 0 0 0 2 0 0 2 2 2 0 2 2 0 2 2 2 2 2 0 0 0 0 2 0 2 2 0 0 0 0 2 2 0 0 2 2 0 0 0 0 0 2 0 2 2 0 0 0 2 2 0 2 0 2 0 2 2 0 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 2 2 2 2 2 2 2 2 0 0 2 0 2 2 0 2 0 2 2 2 2 2 0 0 0 2 0 2 0 0 2 2 0 0 2 0 0 0 2 2 0 0 2 2 2 2 2 0 0 0 2 0 2 0 0 0 0 0 2 0 2 0 2 2 2 0 0 0 0 0 2 0 0 0 0 0 2 0 0 2 2 0 2 2 2 2 2 2 2 0 0 0 0 2 2 2 2 0 2 0 2 0 2 0 2 2 2 0 2 0 0 0 0 0 2 2 2 2 0 0 0 0 0 2 0 0 0 2 2 2 2 0 2 2 2 0 2 0 2 0 2 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 2 0 0 0 2 0 0 0 2 0 0 0 2 0 2 2 2 2 0 0 2 2 2 2 2 0 2 2 0 2 2 0 0 2 2 2 2 2 0 0 2 2 2 2 0 2 0 2 2 2 0 0 0 2 0 2 0 2 2 2 2 0 0 0 0 0 0 0 2 2 2 2 2 0 0 2 0 0 0 2 2 0 0 0 2 2 0 2 2 2 2 0 2 2 0 0 2 2 0 2 2 2 0 0 2 0 2 2 0 0 0 2 0 2 0 2 2 2 0 0 0 2 2 0 0 2 0 0 0 0 0 2 2 2 2 2 2 2 2 2 generates a code of length 79 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 69. Homogenous weight enumerator: w(x)=1x^0+32x^69+219x^70+316x^71+548x^72+684x^73+831x^74+1118x^75+1230x^76+1296x^77+1421x^78+1384x^79+1201x^80+1408x^81+1120x^82+970x^83+867x^84+534x^85+455x^86+274x^87+214x^88+122x^89+39x^90+32x^91+21x^92+18x^93+7x^94+2x^95+12x^96+2x^97+2x^98+1x^100+2x^102+1x^108 The gray image is a code over GF(2) with n=316, k=14 and d=138. This code was found by Heurico 1.16 in 16.9 seconds.