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 X 1 1 1 1 1 0 1 X 1 0 1 0 1 1 X 1 1 0 1 X 1 1 X X 1 X 1 0 1
0 X 0 0 0 0 0 2 2 X X+2 X X X X+2 X 0 X+2 2 X 2 X 0 X 2 X+2 X 0 X+2 2 X+2 0 0 2 0 X X X+2 X X X X X+2 X 2 X+2 X 0 2 0 X 2 X+2 X+2 X+2 0 X X+2 2 X+2 2 X 0 2 X+2 X+2 2 2
0 0 X 0 0 2 X+2 X X X X X X+2 0 0 0 2 2 X+2 X 2 0 0 X+2 2 2 X X+2 0 X X X+2 X X+2 X+2 0 2 0 X+2 X 0 X+2 X+2 X X X X+2 X X 0 2 X+2 2 X+2 2 2 X+2 X+2 2 X+2 X+2 0 X 2 2 X 2 0
0 0 0 X 0 X+2 X+2 X 2 X+2 X+2 0 0 X X 2 X 2 X+2 0 X+2 0 2 X 2 X X 2 X X 0 0 2 X 0 X+2 2 X+2 X 0 0 X+2 X 2 0 2 0 X X X+2 X 2 X 2 2 0 X 2 X 2 0 X X+2 X+2 2 0 0 0
0 0 0 0 X X 2 X+2 X X+2 2 2 X 2 X+2 X X 2 2 X+2 0 X+2 0 X+2 X+2 X+2 0 X+2 0 X 0 2 0 X+2 X 0 2 X+2 X 0 X 2 X X 2 2 0 2 X 2 X X 0 0 X X 0 2 2 0 2 0 X+2 X+2 X+2 X X X+2
generates a code of length 68 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 61.
Homogenous weight enumerator: w(x)=1x^0+70x^61+99x^62+128x^63+143x^64+138x^65+180x^66+194x^67+219x^68+202x^69+183x^70+136x^71+93x^72+72x^73+59x^74+34x^75+21x^76+20x^77+14x^78+20x^79+2x^80+10x^81+9x^82+1x^112
The gray image is a code over GF(2) with n=272, k=11 and d=122.
This code was found by Heurico 1.16 in 30 seconds.