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 X 0 1 1 X 0 1 1 1 1 X 1 1 1 1 0 1 X 1 0 1 1 1 0 X X 1 0 1 1 1 1 1 X 1 0 1 1 2 1 X X X 0 X 0 X+2 0 X+2 0 X+2 0 X+2 2 X+2 0 X+2 X 0 2 2 X+2 X+2 0 0 X+2 X 2 X+2 X 2 0 X+2 X X+2 X X 0 X+2 X+2 2 2 X X X+2 X+2 0 X X X+2 0 X X+2 X+2 2 X 2 X 0 X+2 0 X+2 X+2 X 2 X 0 0 X+2 X+2 2 0 0 2 0 0 0 0 0 0 0 2 0 2 2 2 0 2 0 0 0 0 2 2 2 2 0 2 0 0 2 0 2 0 0 2 2 0 2 0 2 2 2 2 2 2 2 2 2 2 0 2 2 0 2 2 0 2 2 2 2 2 2 2 2 0 0 2 2 0 0 0 2 0 0 0 0 0 0 0 2 0 2 2 0 0 0 0 2 0 0 2 0 0 2 0 0 0 0 2 2 2 0 2 0 0 2 2 0 2 2 0 2 0 0 2 2 2 2 0 2 0 2 2 0 0 2 0 2 0 2 2 0 2 0 2 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 2 2 0 0 2 2 0 0 2 2 0 0 0 0 2 0 0 0 2 2 2 2 0 2 2 2 0 2 0 2 2 0 0 2 0 0 2 2 0 0 2 2 0 0 2 0 2 2 2 0 2 0 0 0 0 0 0 2 0 0 0 2 0 2 0 0 2 0 0 0 0 2 2 2 0 2 2 0 0 2 2 0 2 0 2 2 0 0 0 0 2 2 0 2 0 2 2 2 2 2 2 0 2 0 2 0 0 0 0 2 0 0 2 2 2 2 0 0 2 2 0 0 0 0 0 0 2 0 0 0 0 0 2 0 0 2 0 2 2 2 0 0 2 2 2 2 2 2 2 2 2 2 2 2 0 2 0 2 0 2 2 2 0 2 0 2 0 2 0 0 2 2 0 2 2 2 0 0 0 0 2 2 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 2 0 0 0 2 2 2 2 0 2 2 2 0 0 2 2 2 0 0 2 0 2 2 0 0 0 2 2 0 2 0 0 0 0 0 2 0 2 2 0 0 2 2 0 2 2 2 2 0 2 0 2 0 0 2 2 0 2 0 0 0 0 0 0 0 0 0 2 0 2 2 2 2 0 2 0 0 0 2 2 2 0 0 2 2 2 0 2 0 0 0 2 2 2 0 2 0 2 0 2 0 0 0 2 2 2 0 2 0 2 2 0 2 2 0 2 2 0 0 0 0 2 0 2 2 0 0 generates a code of length 68 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 58. Homogenous weight enumerator: w(x)=1x^0+75x^58+135x^60+364x^62+420x^64+698x^66+725x^68+791x^70+372x^72+286x^74+103x^76+71x^78+21x^80+10x^82+12x^84+5x^86+2x^88+3x^90+1x^94+1x^100 The gray image is a code over GF(2) with n=272, k=12 and d=116. This code was found by Heurico 1.16 in 4.86 seconds.