The generator matrix 1 0 1 1 1 X+2 1 1 2 1 X 1 1 1 X 1 1 2 1 1 0 1 1 X X+2 1 1 1 X 0 1 1 2 1 X X+2 1 1 1 2 X+2 1 1 1 1 1 X 2 X 1 1 1 0 1 1 1 1 1 1 1 2 0 2 1 1 1 1 1 1 2 1 0 1 1 2 1 X X 0 1 1 X+2 X+3 1 0 X+1 1 X 1 3 X X+3 1 2 1 1 0 1 1 X+2 X+1 1 1 1 X X+3 1 1 0 3 1 3 1 1 X+3 X+1 2 1 1 0 2 X+1 3 X+3 1 1 1 X+2 X+2 1 1 X X+3 1 X 3 X X+3 1 1 1 0 1 X+1 X+2 2 X+2 1 3 1 0 3 0 0 1 0 0 0 X 0 X+2 0 X+2 2 X X X 2 X+2 X X+2 X+2 X X 0 0 2 0 2 X 0 X+2 2 X+2 0 2 2 2 X+2 2 X+2 X+2 0 X+2 X 2 0 2 X 0 X 2 0 X X 0 X+2 0 X+2 0 X X+2 0 X+2 X+2 2 0 2 0 2 X+2 X 0 0 X 0 X X+2 X+2 X X X X 2 0 0 0 2 0 0 0 2 2 0 2 0 0 0 2 0 0 2 0 0 0 0 0 2 2 2 0 2 2 2 2 2 2 0 0 0 2 0 2 0 2 0 2 2 0 0 2 0 2 2 0 0 2 0 2 2 2 0 2 0 0 2 0 0 2 0 2 2 2 2 2 0 0 0 2 0 0 2 0 0 0 0 2 0 0 0 0 2 0 0 0 2 2 2 0 2 2 0 2 2 2 2 0 2 0 2 2 2 2 0 0 2 0 2 2 2 2 2 2 0 2 0 2 2 2 0 2 0 0 0 2 2 0 0 2 2 2 2 0 0 2 0 0 0 2 0 2 2 2 2 0 2 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 0 0 2 2 2 0 2 0 0 2 2 0 2 2 2 2 0 2 0 2 2 2 2 2 0 0 2 2 2 0 0 0 2 2 0 2 2 2 0 2 0 2 0 2 2 0 2 0 2 0 0 0 2 2 2 0 0 0 2 0 0 0 0 0 0 0 0 2 0 2 0 0 0 0 2 2 2 2 0 0 2 2 2 2 2 2 0 2 0 0 0 2 2 0 0 0 0 0 2 2 0 2 2 2 0 0 2 2 2 0 2 2 0 0 0 2 0 0 2 2 0 0 2 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 2 generates a code of length 78 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 70. Homogenous weight enumerator: w(x)=1x^0+79x^70+104x^71+210x^72+212x^73+294x^74+336x^75+367x^76+388x^77+317x^78+336x^79+266x^80+348x^81+237x^82+240x^83+128x^84+76x^85+63x^86+8x^87+35x^88+18x^90+7x^92+13x^94+7x^96+3x^98+2x^100+1x^104 The gray image is a code over GF(2) with n=312, k=12 and d=140. This code was found by Heurico 1.16 in 1.36 seconds.