The generator matrix

 1  0  0  1  1  1  X  1 X+2  1  1  X  1 X+2  1  X  2  1  1  X  1  1  0  0  1  1  1  2  2  1  1 X+2  1 X+2  0 X+2  1  1  1  1  0  X  1  X  1 X+2  1  1  1  1  1  0  1  1  1  0 X+2  0  1  X  2  2  1  1  1  X  1  1
 0  1  0  0  1 X+3  1  2  0  2 X+3  1 X+1  1  1 X+2  1  X  X  1  X  3  X  1 X+1  1  2  1  1 X+3 X+3  1  X  0  2  1  2  0 X+3 X+1  1  0 X+3  1  X  1 X+2  0 X+1  X  X  1  0 X+1  1  1  X  1 X+3  1  1 X+2  0  2  2  1 X+1  0
 0  0  1  1 X+1  0  1 X+1  1  X X+1  X  X X+1  3  1  X X+2  0  2 X+1 X+2  1 X+1  0  1  1  1  0  2  3 X+3 X+1  1  1 X+1  X  3  X X+3  1  1  1 X+2  3  2  0  X  1  0  3 X+1  1  0  0  3  1 X+2  0  2  3  1  3 X+1  1  3 X+2  2
 0  0  0  X  X X+2  2 X+2  0  0  X  2  X  0 X+2  0  0  2  2  2 X+2  X  0  2 X+2  0  0  X X+2  2  2  X  2 X+2 X+2 X+2  2  2  0  0  0 X+2  X  X  X X+2 X+2  X  0 X+2  0 X+2  0  2  X X+2 X+2 X+2 X+2  0  X  0 X+2 X+2  X  0  2  0
 0  0  0  0  2  0  0  2  2  2  0  2  2  0  0  2  0  0  2  2  0  0  0  2  2  2  0  2  0  2  0  2  2  2  0  0  0  2  0  0  2  0  2  2  0  0  0  2  2  0  0  0  2  0  2  2  0  0  2  0  2  0  2  2  2  2  2  2
 0  0  0  0  0  2  2  0  0  0  0  0  0  0  2  2  2  2  2  2  2  0  2  0  2  2  2  0  2  0  0  2  0  2  0  2  0  2  0  2  0  2  2  0  0  0  2  2  2  0  0  2  0  2  2  2  0  0  0  0  2  0  2  2  0  2  0  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+60x^60+178x^61+406x^62+478x^63+747x^64+550x^65+777x^66+668x^67+813x^68+602x^69+738x^70+522x^71+529x^72+320x^73+318x^74+166x^75+135x^76+66x^77+54x^78+16x^79+15x^80+10x^81+9x^82+6x^83+4x^84+2x^85+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 3.43 seconds.