The generator matrix

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

generates a code of length 68 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 59.

Homogenous weight enumerator: w(x)=1x^0+172x^59+596x^60+1030x^61+1446x^62+1776x^63+2165x^64+2352x^65+2725x^66+2664x^67+2933x^68+2784x^69+3043x^70+2210x^71+2058x^72+1642x^73+1312x^74+850x^75+433x^76+290x^77+137x^78+86x^79+36x^80+10x^81+9x^82+2x^83+4x^85+2x^88

The gray image is a code over GF(2) with n=272, k=15 and d=118.
This code was found by Heurico 1.13 in 16.7 seconds.