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 1 1 1 X 2 2 0 2 0 2 2 0 1 X X 1 2 1 1 2 1 1 X 1 1 0 1 X X 1 1 1 1 1 2 1 1 2 X 1 1 0 X 0 0 0 0 0 0 0 X+2 X X X X 2 X+2 0 X X X+2 2 X+2 X 2 X X 0 0 X+2 2 0 2 X X+2 X 0 2 X+2 X+2 X 2 X 2 0 X X 2 0 2 X+2 2 X 0 2 0 2 X X 2 0 2 0 X+2 2 X 2 X 2 X+2 2 0 X+2 X 2 X X+2 2 0 0 X 0 0 0 X X+2 X 2 X X+2 0 0 X X 2 X+2 X 2 X X X X 2 2 0 X+2 X 0 0 X+2 X X+2 X 2 X+2 0 2 X+2 X 0 X X X 2 2 X X+2 X+2 X+2 X+2 2 0 0 X X X X+2 X 2 X 0 0 X+2 X 2 X+2 X 0 0 0 2 X X X+2 0 0 0 0 X 0 X X X 0 X+2 2 X X+2 0 X 0 X X X+2 0 0 2 X X X+2 2 0 X+2 2 X+2 2 X 0 0 X 2 2 0 X X+2 X+2 X+2 2 X 2 2 0 2 X+2 X+2 X X X X+2 0 0 2 0 X 0 2 X+2 2 2 2 2 X X+2 X+2 0 X X+2 X+2 X+2 X+2 X+2 0 0 0 0 0 X X 0 X X+2 X 0 X 2 X+2 X+2 X 0 X 0 0 2 2 0 X+2 X X+2 2 0 X+2 0 X+2 2 0 X+2 X+2 X X X+2 0 X+2 2 2 2 2 X X+2 X 2 X+2 0 X+2 2 0 0 X+2 X+2 X+2 X+2 X X X+2 0 0 X+2 X 0 X X+2 2 2 X+2 2 2 0 X X+2 X 0 0 0 0 0 2 0 0 0 0 0 0 0 2 2 2 2 2 0 0 2 0 2 0 2 0 2 2 0 0 0 2 2 0 2 2 2 2 2 0 0 2 2 2 0 2 0 0 2 0 0 2 0 2 0 2 2 2 0 2 2 0 2 0 2 2 0 0 0 0 2 2 0 2 0 2 0 0 0 0 0 0 0 2 0 2 0 2 2 2 2 0 0 0 2 2 2 2 0 2 2 2 0 0 2 0 2 2 0 0 2 0 2 2 0 2 2 0 0 2 0 0 2 0 0 2 0 0 0 0 2 2 2 2 0 0 0 2 2 0 2 0 2 0 0 2 2 2 2 0 2 2 0 2 generates a code of length 77 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 66. Homogenous weight enumerator: w(x)=1x^0+56x^66+76x^67+147x^68+186x^69+275x^70+308x^71+381x^72+490x^73+493x^74+648x^75+811x^76+764x^77+610x^78+648x^79+536x^80+422x^81+321x^82+280x^83+209x^84+128x^85+119x^86+76x^87+69x^88+48x^89+33x^90+12x^91+17x^92+10x^93+12x^94+5x^96+1x^114 The gray image is a code over GF(2) with n=308, k=13 and d=132. This code was found by Heurico 1.16 in 7.08 seconds.