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 1 1 0 X X X 2 2 X X 1 0 1 X 1 X 1 1 X 1 X 0 1 1 1 X X X 2 1 1 X 1 X 1 1 1 0 2 0 X 0 0 0 0 0 0 0 X+2 X X X X X+2 X 2 X 0 0 X+2 2 X 2 X X 2 0 2 X+2 2 X+2 0 2 X X+2 X+2 X X X 2 X X+2 X+2 2 X 2 2 2 X+2 X X X X+2 X X+2 0 2 X 2 2 2 0 X+2 X 0 0 0 2 X+2 2 X+2 X+2 X+2 X+2 0 X X 0 0 X 0 0 0 X X+2 X 2 X X+2 0 0 X 2 X X 2 X+2 2 X X+2 X+2 0 X+2 2 0 0 X+2 0 2 0 0 X+2 X+2 X+2 2 2 0 2 X+2 X+2 0 X X+2 X X+2 X 0 X 2 0 X X 2 X+2 X 0 0 X X+2 2 0 X+2 0 0 X X+2 2 2 2 0 X+2 X 2 0 X+2 0 0 0 X 0 X X X 0 X+2 2 X X+2 0 0 X+2 X+2 X X+2 0 X X 0 2 0 X 2 2 X+2 X X 2 0 0 X+2 X+2 2 X+2 0 0 2 0 2 2 X 0 X+2 2 0 X+2 X+2 X+2 X+2 X+2 X X X+2 0 X X+2 X+2 2 X+2 X+2 X+2 2 X+2 X+2 0 X 2 X+2 2 2 X 2 2 X 0 0 0 0 X X 0 X X+2 X 0 X 2 X+2 X 2 0 0 0 X X+2 X+2 X+2 0 2 X+2 X 2 X X X X X 2 X 2 0 X X+2 X+2 2 X X 0 X+2 2 0 X 0 0 2 X 2 0 X X+2 X 0 X+2 X 0 X X 2 X+2 X 0 X 2 0 X+2 X+2 2 0 X+2 2 0 X 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 2 2 2 2 2 2 2 0 2 0 2 0 2 2 0 2 2 0 2 0 0 0 2 0 2 2 0 2 2 2 0 2 2 2 2 2 0 0 0 0 0 0 2 2 0 2 2 0 2 0 0 2 2 2 2 0 2 2 2 2 0 0 0 0 0 0 0 2 0 2 0 2 2 2 2 2 0 0 2 0 2 0 0 0 2 2 2 2 2 2 0 2 0 2 0 0 0 0 2 2 0 2 0 2 2 2 2 2 2 2 0 2 2 2 0 0 2 0 2 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 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+194x^68+4x^69+402x^70+68x^71+565x^72+152x^73+684x^74+348x^75+867x^76+440x^77+926x^78+524x^79+828x^80+248x^81+562x^82+196x^83+494x^84+52x^85+264x^86+16x^87+197x^88+90x^90+45x^92+16x^94+8x^96+1x^112 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 7.47 seconds.