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  0  1  X  X  1  X  1  1  X  1  1  X  1  0  1  1  2  1  0  X  1  1  0  1  1  X  1
 0  X  0  X  0  0  X X+2  0  2  X X+2  0 X+2  2 X+2  X  0  2  X  2 X+2  0 X+2  0  2  2  X  X  0  X  X  0  2  X X+2  0  2  0  0 X+2  X X+2 X+2  2  X  X X+2  2 X+2  2 X+2  0  0  0  2  X  0  X  X  X  X X+2  0 X+2 X+2 X+2  0
 0  0  X  X  0 X+2  X  0  2  X  X  0  2 X+2  X  2  X  0 X+2  0  0  2 X+2  X  0  0  X  X  2 X+2 X+2  2  0  X  X  0  0 X+2 X+2  2  2  2 X+2  0  X  X  X  0  X  2  0  X X+2  2  X  0  X  X X+2  2  X X+2 X+2  X X+2  0  0  0
 0  0  0  2  0  0  0  2  2  2  0  0  2  2  0  0  0  2  2  2  2  0  0  0  2  2  0  0  0  0  0  0  0  0  2  2  2  2  2  0  0  0  2  0  2  2  2  0  2  0  0  0  0  0  2  0  2  2  2  2  0  0  2  2  0  2  0  0
 0  0  0  0  2  0  0  0  0  0  2  0  2  2  2  2  0  2  2  2  0  2  2  2  2  0  0  2  0  2  0  2  0  0  2  0  2  0  0  2  0  2  0  2  0  2  0  0  2  0  0  2  0  0  2  0  0  2  2  0  0  2  2  0  2  2  2  0
 0  0  0  0  0  2  0  0  0  2  2  2  2  0  0  0  2  0  2  0  2  2  2  0  0  0  2  0  0  2  0  0  0  0  2  2  2  0  2  2  0  2  2  0  2  0  0  2  0  2  2  2  0  2  0  0  2  2  0  0  0  2  2  0  2  0  0  0
 0  0  0  0  0  0  2  2  2  2  2  0  2  0  0  0  2  2  2  2  2  0  0  2  0  0  2  0  2  2  0  2  2  2  2  2  0  0  0  2  2  0  0  0  2  2  0  2  2  2  2  0  2  0  2  2  2  2  2  0  0  0  0  2  2  2  2  0

generates a code of length 68 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+49x^60+48x^61+81x^62+108x^63+124x^64+160x^65+171x^66+228x^67+207x^68+200x^69+182x^70+130x^71+91x^72+86x^73+45x^74+34x^75+20x^76+14x^77+27x^78+10x^79+20x^80+2x^81+4x^82+2x^83+2x^85+1x^86+1x^110

The gray image is a code over GF(2) with n=272, k=11 and d=120.
This code was found by Heurico 1.16 in 0.513 seconds.