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 X 1 1 1 1 1 1 0 1 1 1 1 1 X 1 1 X X 2 1 0 1 1 1 X 1 2 1 1 0 X 0 X+2 0 X+2 0 X+2 2 X+2 0 X+2 X 0 2 X+2 2 X+2 2 X 0 0 X+2 X 0 2 0 2 X+2 X+2 X X 0 0 0 2 X+2 X+2 X+2 X X+2 0 X+2 X+2 0 X X+2 X X+2 2 X 2 2 X+2 2 2 X+2 0 2 2 X X X 2 2 X+2 0 2 X+2 0 0 2 0 0 0 0 0 2 0 0 2 2 2 2 0 2 2 0 2 0 2 0 0 0 2 2 0 0 0 0 0 0 0 0 2 0 2 2 0 2 2 0 0 2 2 2 2 2 0 2 0 2 0 2 0 0 2 0 2 2 2 2 2 0 2 2 2 2 0 0 0 2 0 0 0 0 0 0 2 2 0 2 0 2 0 2 0 0 0 0 2 2 0 2 0 2 0 2 2 0 0 2 0 2 0 2 2 2 0 0 2 2 2 2 0 0 2 2 0 2 2 0 0 0 0 2 0 2 2 2 0 2 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 2 0 2 0 2 0 0 2 2 2 2 2 0 0 0 2 2 0 0 0 0 2 2 0 2 0 2 2 0 2 2 2 2 0 0 2 2 0 2 0 0 0 2 2 2 0 0 0 2 2 2 0 2 0 2 0 0 0 0 0 2 0 0 0 2 0 0 2 0 0 2 0 2 0 0 0 0 0 2 2 2 2 2 0 0 2 2 0 0 2 2 2 2 2 0 0 2 0 0 2 2 2 0 0 0 2 0 0 2 2 2 2 0 0 2 2 0 0 2 2 0 2 0 0 0 0 0 0 0 0 2 0 2 0 2 0 0 0 2 0 0 0 2 0 2 0 2 2 0 2 2 0 2 0 0 2 0 2 2 0 0 0 2 2 0 2 2 0 2 2 0 0 2 0 2 0 2 2 2 0 2 2 0 0 2 0 2 0 0 2 2 0 0 0 0 0 0 0 0 0 2 0 2 2 2 2 2 0 2 0 0 0 0 2 2 0 2 0 0 0 0 2 2 0 0 2 2 0 0 2 2 0 0 0 2 2 0 2 2 2 0 0 0 2 0 2 0 2 0 0 2 2 2 2 0 0 2 2 0 0 2 2 generates a code of length 69 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 61. Homogenous weight enumerator: w(x)=1x^0+90x^61+51x^62+103x^64+170x^65+124x^66+128x^67+220x^68+276x^69+273x^70+128x^71+164x^72+132x^73+36x^74+4x^76+82x^77+25x^78+16x^80+18x^81+3x^86+3x^88+1x^120 The gray image is a code over GF(2) with n=276, k=11 and d=122. This code was found by Heurico 1.16 in 12.3 seconds.