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 X 1 0 X X X 1 1 1 0 1 X 1 0 2 1 X 2 1 1 1 1 1 1 X X 1 0 1 X X 2 X 1 X 1 2 0 2 1 0 0 X 0 X 0 0 X X+2 0 2 X 0 X+2 2 X+2 X X+2 0 X 0 X 2 0 X X 0 X+2 0 X 2 X X+2 X 0 X 2 X 0 X 2 X X 0 2 X X 2 0 0 2 X+2 X+2 X 0 0 X X 2 X 0 X 0 2 X X X X+2 X 0 0 X X 0 X+2 X 0 0 X X 2 2 X+2 X 2 0 0 X 0 X X X+2 0 X+2 X+2 X X+2 2 X X+2 0 X X 0 X 2 0 X X 2 X+2 0 X X X+2 0 2 0 0 2 2 X+2 0 X X X+2 X+2 0 X X+2 X+2 0 2 X+2 0 2 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 2 0 2 2 2 0 0 2 2 0 0 0 2 2 2 0 2 2 2 0 0 2 0 0 2 2 0 0 2 0 2 0 2 0 0 2 2 0 2 2 2 0 2 2 0 2 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 2 2 0 2 0 2 2 2 2 2 2 0 0 0 0 0 0 2 2 0 2 2 2 0 0 0 2 2 2 2 2 0 0 2 0 0 0 0 2 2 2 2 2 2 0 2 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 2 2 2 0 2 0 2 2 0 2 0 2 0 2 2 0 2 2 0 2 0 2 0 2 2 0 0 2 2 2 0 2 0 0 0 0 0 2 0 2 0 2 0 2 2 2 0 0 0 0 0 0 0 2 0 0 0 2 0 0 0 0 0 2 2 2 2 2 2 0 0 0 0 0 2 2 0 2 0 2 2 2 0 2 2 0 2 0 2 0 2 2 2 0 2 0 0 0 2 2 2 2 2 0 0 2 2 0 2 0 2 0 2 0 0 0 0 0 0 0 0 0 2 0 2 2 2 2 0 0 0 2 0 0 2 2 0 2 0 2 2 2 2 2 2 0 2 2 2 2 0 0 0 2 2 2 2 0 2 0 2 2 0 2 2 2 0 0 2 0 0 0 0 0 0 2 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 2 2 2 2 2 0 2 2 0 0 0 2 2 2 2 2 2 0 0 0 2 2 0 2 2 2 0 2 0 0 0 0 0 2 0 0 0 2 2 2 2 0 2 2 2 2 2 0 2 2 0 0 2 0 0 2 generates a code of length 68 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 57. Homogenous weight enumerator: w(x)=1x^0+36x^57+99x^58+128x^59+224x^60+196x^61+336x^62+376x^63+443x^64+572x^65+662x^66+726x^67+683x^68+750x^69+550x^70+588x^71+506x^72+392x^73+300x^74+200x^75+131x^76+76x^77+73x^78+28x^79+45x^80+24x^81+18x^82+2x^83+9x^84+2x^85+8x^86+4x^88+1x^90+1x^92+1x^94+1x^96 The gray image is a code over GF(2) with n=272, k=13 and d=114. This code was found by Heurico 1.16 in 16.5 seconds.