The generator matrix

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

generates a code of length 68 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+248x^58+682x^59+1167x^60+1882x^61+2597x^62+2976x^63+4148x^64+4412x^65+5646x^66+5788x^67+6264x^68+5780x^69+5702x^70+4948x^71+4178x^72+3176x^73+2306x^74+1354x^75+1111x^76+562x^77+321x^78+132x^79+83x^80+28x^81+12x^82+24x^83+6x^84+2x^88

The gray image is a code over GF(2) with n=272, k=16 and d=116.
This code was found by Heurico 1.13 in 63.9 seconds.