The generator matrix

 1  0  0  0  1  1  1  X X+2  1  1  1 X+2  0  1  0  2  1  1  0  2  1  1  X  1  1  1  X  1  0  1  X  2  2  1  X  1  0  1  0  1  1  0  1  2 X+2  X  1  1  0  1  0  1 X+2  1  1  2  1 X+2  0  X  1  1  1 X+2  1  1  1
 0  1  0  0  X  0 X+2 X+2  1  3  3  3  1  1 X+1 X+2  1 X+3  2  1  1  0 X+1  1 X+3  0  1 X+2  0  X  3  1  1  X  2  1  1  1  1  X  3 X+2  2  X  1  2 X+2 X+1  2  1  0  0 X+3  1 X+3  X  0  3  1  1  1 X+2  0  3  X  3  2  X
 0  0  1  0  X  1 X+3  1  3 X+2  3  2  0 X+3  1  1  0  0  X  1  X  X X+3 X+3  1 X+3  X  1  3  0 X+3  X X+2  1  3 X+3  2  2  2 X+2  1  0  1 X+1 X+3  0 X+2  1 X+3  1 X+1  1  2  2 X+1  X  1 X+1 X+3  1  0  1 X+1 X+3  1  X  3 X+3
 0  0  0  1 X+1  1  X X+3  0  2  0 X+3 X+3 X+1  3  0 X+2 X+2 X+2  0  1 X+3 X+1  3  2  1 X+1  3 X+2  1  3  2 X+2 X+3  1 X+3  3 X+3  0  1  1  3  X X+2  1  1  1  X  1  X  2  1  2 X+3  3  3  2  3 X+3  1  3 X+3 X+2 X+3  0 X+2 X+1  0
 0  0  0  0  2  0  2  2  2  2  0  0  2  0  2  0  0  2  0  2  2  2  2  0  0  0  0  2  2  2  0  2  2  0  2  0  2  0  0  0  0  0  2  0  2  0  0  0  2  0  0  2  2  0  2  0  2  2  2  0  0  0  0  2  0  0  2  0
 0  0  0  0  0  2  2  2  2  0  2  0  0  2  2  2  2  2  2  0  2  2  0  0  0  0  2  0  0  0  2  2  0  2  0  0  2  0  0  0  0  0  2  2  0  2  0  2  0  0  0  0  2  2  0  2  2  2  2  2  0  2  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+272x^60+456x^61+802x^62+1000x^63+1110x^64+1216x^65+1318x^66+1436x^67+1373x^68+1512x^69+1310x^70+1252x^71+965x^72+784x^73+570x^74+388x^75+315x^76+128x^77+114x^78+20x^79+20x^80+12x^82+8x^84+2x^86

The gray image is a code over GF(2) with n=272, k=14 and d=120.
This code was found by Heurico 1.16 in 13.8 seconds.