The generator matrix 1 0 1 1 1 X+2 1 1 0 1 1 X+2 0 1 1 1 X+2 1 1 1 X 0 1 1 1 X+2 1 1 1 0 1 1 1 1 1 2 1 X+2 X+2 1 1 1 1 0 1 1 1 1 1 0 1 1 1 X+2 1 1 1 X+2 1 1 X+2 1 X 0 1 0 2 2 1 0 0 1 1 2 1 1 1 1 0 1 X+1 X+2 1 1 0 X+1 1 X+2 3 1 1 X+2 X+1 0 1 3 2 3 1 1 X+2 X+1 X 1 X+3 0 3 1 X+2 3 0 X+1 X+3 1 0 1 1 X+2 X 3 X+1 1 0 X+2 X+1 3 0 1 X 3 1 1 3 0 2 1 X+2 X+3 1 X+2 1 1 X+1 1 1 1 3 1 1 X X+1 X 1 0 X+2 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 2 0 2 2 0 2 2 2 2 2 2 0 0 2 0 2 2 2 0 2 2 0 2 0 0 2 0 0 2 2 0 0 2 2 0 2 0 0 2 2 2 0 0 0 2 2 0 2 0 0 0 0 0 2 0 2 0 2 2 0 2 0 2 2 0 0 0 2 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 0 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 2 0 2 0 0 2 2 2 0 2 2 2 2 2 2 2 2 0 0 0 0 0 0 2 0 2 0 2 0 2 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 2 0 0 2 2 0 2 2 0 0 2 0 2 0 0 2 2 0 2 2 0 0 0 0 2 0 2 2 0 0 0 2 2 2 2 0 0 0 2 2 0 2 2 2 2 0 0 2 0 0 0 2 2 2 0 2 2 0 2 0 0 2 0 0 0 0 0 0 0 0 0 2 0 0 0 0 2 2 2 0 2 0 0 2 0 0 0 2 2 0 2 0 2 0 0 2 0 2 0 2 0 0 2 2 0 0 2 2 0 0 0 2 0 2 2 0 2 2 0 2 2 2 0 0 0 0 2 2 2 0 2 2 0 2 0 0 0 0 0 2 0 0 2 2 0 0 0 0 0 0 2 0 0 2 2 0 0 2 2 0 0 2 2 0 0 2 0 0 2 2 2 0 0 0 2 2 0 0 2 2 0 2 0 0 2 2 2 2 0 0 2 0 0 2 0 2 2 2 0 0 0 2 2 0 2 2 2 2 0 2 2 0 2 0 0 2 2 0 2 2 0 0 0 0 0 0 0 0 0 2 0 2 0 0 0 2 2 2 2 0 2 0 2 2 2 0 0 0 0 2 2 2 2 0 2 0 2 0 2 2 0 2 2 0 0 0 0 0 0 2 2 2 0 2 2 0 0 0 2 2 2 0 2 0 0 2 2 0 0 2 0 0 2 2 0 2 2 0 2 2 0 0 0 0 0 0 0 0 2 0 2 2 0 0 2 2 0 0 2 2 2 0 2 2 2 2 0 0 2 2 0 2 2 2 0 2 0 2 2 2 0 2 0 0 2 2 2 0 2 2 2 2 0 0 2 0 0 2 0 0 0 2 0 0 0 2 0 0 0 2 2 2 0 2 2 0 0 0 generates a code of length 78 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+110x^68+24x^69+150x^70+144x^71+489x^72+288x^73+610x^74+464x^75+839x^76+624x^77+800x^78+592x^79+832x^80+480x^81+584x^82+304x^83+429x^84+120x^85+154x^86+32x^87+68x^88+6x^90+21x^92+11x^96+9x^100+7x^104 The gray image is a code over GF(2) with n=312, k=13 and d=136. This code was found by Heurico 1.16 in 5.36 seconds.