The generator matrix

 1  0  0  1  1  1  X  1  1 X+2  1  1  X X+2  X  0  1  1  1  1 X+2 X+2  1  1  1  1  0  0  1  X  2  1  1 X+2  2  1  X  1  2 X+2  2  2  1 X+2  1  1  0  1  1  1 X+2  0  1  1  1  1  1 X+2  1  1  1  1  1  1  0 X+2  0  1
 0  1  0  X  1 X+3  1 X+2  0  2  1 X+1 X+2  1  1  1 X+2 X+3  0  3  1  1  3  X  0 X+1  1  0 X+2  1  1 X+2  1  1  1 X+3 X+2 X+3  1  0  X  1  X  2  2  2  1  3  0  2  1 X+2  X X+2  2 X+3  3  1  2  3 X+2  X X+1  0  1  1  1 X+2
 0  0  1  1 X+3 X+2  1 X+1 X+2  1  1  0  1 X+1  X X+1  2  1 X+3 X+2  0  X  0  X  3 X+3 X+1  1 X+3  1  2  2  0 X+1 X+2  0  1  1  1  1  1 X+1  0  1  0 X+2  1  2  1 X+3 X+3  1 X+2  3 X+2  0  0 X+1 X+3  1 X+3 X+1 X+1  0  2  X  X X+1
 0  0  0  2  0  0  0  0  2  2  0  0  0  2  2  2  2  0  0  2  2  0  0  2  0  2  0  2  2  0  0  2  2  0  2  2  0  0  0  2  0  0  2  0  2  0  0  0  2  0  2  2  0  2  2  2  2  2  2  2  0  0  2  0  0  2  0  2
 0  0  0  0  2  0  0  0  0  0  0  2  2  2  2  2  0  2  2  0  0  2  0  2  0  2  0  2  0  0  0  0  2  0  2  2  2  0  2  2  2  2  0  2  0  0  2  2  0  2  0  2  2  2  2  2  0  2  0  2  0  2  0  2  2  0  0  2
 0  0  0  0  0  2  0  0  0  0  0  2  0  0  0  0  0  0  0  2  0  0  0  2  2  2  2  2  2  2  2  2  0  0  2  2  2  0  0  0  2  2  2  0  2  0  2  0  2  2  0  2  2  0  2  0  0  2  2  0  2  0  2  2  2  2  0  2
 0  0  0  0  0  0  2  0  0  0  0  0  0  2  0  0  2  2  2  2  2  2  2  2  2  2  0  0  2  2  0  0  0  0  2  0  0  2  0  0  2  0  2  2  0  2  2  2  0  2  0  2  0  0  0  2  0  2  2  2  2  0  0  0  0  2  0  2

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+54x^60+226x^61+350x^62+522x^63+614x^64+676x^65+748x^66+700x^67+751x^68+692x^69+668x^70+592x^71+454x^72+368x^73+242x^74+204x^75+144x^76+74x^77+36x^78+22x^79+27x^80+12x^81+2x^82+8x^83+3x^84+2x^86

The gray image is a code over GF(2) with n=272, k=13 and d=120.
This code was found by Heurico 1.16 in 3.46 seconds.