The generator matrix 1 0 1 1 1 X+2 1 1 2 1 X 1 1 2 1 1 1 X 1 1 0 X+2 1 1 1 X 1 1 1 X+2 1 1 2 1 0 1 0 1 1 X 1 1 0 X X X 1 1 1 2 1 1 0 1 1 2 1 1 1 1 1 1 1 1 X+2 1 2 0 0 0 1 1 1 1 2 X 1 1 1 0 1 1 0 X+3 1 X X+1 1 3 1 X+2 X+1 1 0 X+2 3 1 X+2 X+3 1 1 0 3 2 1 3 0 0 1 1 X+1 1 0 1 X+2 1 0 X 1 3 X+1 1 1 1 1 2 X+3 3 1 X+1 1 1 X+2 X+3 1 X+3 2 0 X X+1 X+2 2 X 1 1 1 1 0 1 3 2 2 X+1 X 2 1 1 2 0 0 X 0 X+2 0 0 X 0 X+2 0 0 0 X X X 2 X X+2 2 X X 2 0 X 2 2 X X X+2 X+2 X X 0 X X 0 2 X+2 X X 0 0 2 X X+2 X+2 X+2 X 0 0 2 X+2 X+2 2 X X+2 2 2 2 0 0 X 0 X+2 2 X 2 2 0 X X+2 X X 2 2 2 X+2 X 0 0 0 X 0 0 X X X X X+2 2 0 2 X+2 X+2 X X 0 X+2 X 0 2 2 2 X 0 X 2 X+2 2 X+2 0 X X 2 2 X X 2 X 2 X X+2 0 0 X+2 X X+2 2 X 2 X+2 X X 0 X 2 X 2 0 0 X+2 X+2 X X+2 X X+2 X 2 X+2 2 2 X X X 2 X 0 0 0 0 0 2 0 0 0 0 0 2 2 2 2 2 0 0 0 2 2 0 0 2 2 0 2 0 2 0 2 2 0 2 0 2 2 2 0 0 2 0 0 0 2 2 2 0 2 2 0 2 0 0 0 2 0 0 2 2 0 0 2 2 0 2 0 0 2 0 2 2 0 0 0 2 2 2 2 0 0 0 0 0 0 2 0 0 2 2 2 0 2 0 2 2 0 2 2 2 2 2 0 0 0 0 2 0 0 0 0 0 2 0 2 2 0 2 0 2 0 0 2 2 0 0 0 2 2 0 2 0 0 0 0 0 2 0 0 0 0 2 0 2 2 0 2 0 0 2 2 2 2 0 2 0 0 2 2 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 2 0 0 0 2 2 2 2 2 2 2 2 2 0 0 2 2 2 2 2 0 2 2 0 0 2 2 2 2 2 0 0 2 0 0 0 0 0 2 0 0 2 0 0 2 0 2 0 0 0 2 2 2 2 2 0 2 0 0 0 2 2 2 0 0 0 0 0 0 0 0 2 2 2 2 0 0 0 0 0 2 2 0 0 0 2 2 2 2 0 2 0 0 2 2 0 0 2 2 2 0 2 0 2 2 0 2 2 0 2 2 2 0 2 0 0 0 2 0 2 2 2 2 0 2 2 0 0 2 0 2 2 2 2 2 0 0 0 0 2 0 2 0 generates a code of length 79 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+75x^68+112x^69+174x^70+408x^71+342x^72+836x^73+585x^74+1242x^75+833x^76+1704x^77+1103x^78+1750x^79+1077x^80+1562x^81+842x^82+1374x^83+554x^84+758x^85+282x^86+294x^87+140x^88+118x^89+57x^90+48x^91+41x^92+26x^93+23x^94+4x^95+8x^96+4x^97+4x^98+1x^100+2x^102 The gray image is a code over GF(2) with n=316, k=14 and d=136. This code was found by Heurico 1.16 in 19.8 seconds.