The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 2 X X X 1 X X X X 1 0 1 1 1 X 0 X 1 2 0 1 X 1 1 1 X X 1 1 1 X 0 1 X X 1 1 1 0 X 1 1 0 X 0 0 0 0 0 0 0 X+2 X X X X X+2 X 2 X 0 2 0 2 2 X 2 2 X+2 0 0 X+2 X+2 X 0 0 X X+2 X+2 X X 2 0 2 X+2 X 0 X+2 X 0 X X+2 X+2 X+2 X X X+2 X X 0 2 X X 2 0 X X+2 X 2 X X X X X+2 0 X+2 X+2 0 X X 0 0 0 X 0 0 0 X X+2 X 2 X X+2 0 0 X 2 X X 2 2 X+2 X+2 0 X X+2 2 X X+2 X+2 0 2 X+2 X+2 2 2 X+2 X+2 X+2 X+2 X+2 2 2 X 2 X+2 0 X X X X+2 2 X+2 X 2 X 0 X X X X 0 2 0 2 X X X+2 X 2 0 2 X 0 2 2 X 0 0 0 0 0 0 X 0 X X X 0 X+2 2 X X+2 0 0 X+2 X+2 X X+2 2 0 2 X 0 X 2 X X+2 0 2 2 0 2 2 X X X+2 0 2 2 2 X 0 X X X 0 0 0 0 X+2 X 2 X+2 X 2 X+2 0 X 0 X X+2 2 X+2 X+2 2 0 0 2 2 2 X X 0 X X+2 0 2 0 0 0 0 0 X X 0 X X+2 X 0 X 2 X+2 X 2 0 0 0 X+2 X 2 X+2 X X+2 2 X+2 0 0 X 2 2 2 0 X 2 0 2 0 X X+2 0 X 2 0 X+2 0 X X X 0 X+2 0 0 0 2 0 X X X 2 X+2 X+2 2 X X X 2 2 X+2 2 X X+2 0 0 X 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 2 2 2 2 0 2 0 2 2 2 2 2 0 0 2 2 0 2 0 0 2 2 2 2 0 0 2 0 2 0 0 2 0 2 0 0 2 0 0 2 2 2 2 2 0 2 2 0 2 0 0 2 2 0 0 0 2 2 0 0 2 0 0 0 0 0 0 0 2 0 2 0 2 2 2 2 2 0 0 2 0 2 2 2 2 0 0 0 0 0 0 2 2 2 2 2 0 2 0 0 2 0 2 2 0 2 2 0 0 2 0 2 2 2 0 0 0 0 0 0 2 2 0 0 2 0 0 0 0 2 2 0 2 2 0 2 2 0 0 0 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+50x^68+84x^69+161x^70+260x^71+242x^72+400x^73+395x^74+458x^75+536x^76+584x^77+688x^78+626x^79+729x^80+580x^81+525x^82+420x^83+334x^84+308x^85+195x^86+212x^87+104x^88+72x^89+65x^90+62x^91+44x^92+16x^93+11x^94+6x^95+4x^96+4x^97+7x^98+4x^99+4x^100+1x^110 The gray image is a code over GF(2) with n=316, k=13 and d=136. This code was found by Heurico 1.16 in 7.35 seconds.