The generator matrix

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

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+78x^59+312x^60+402x^61+719x^62+832x^63+1241x^64+1060x^65+1496x^66+1272x^67+1767x^68+1254x^69+1581x^70+1040x^71+1032x^72+748x^73+707x^74+298x^75+225x^76+94x^77+88x^78+56x^79+25x^80+24x^81+17x^82+8x^83+4x^84+2x^85+1x^88

The gray image is a code over GF(2) with n=272, k=14 and d=118.
This code was found by Heurico 1.16 in 13.8 seconds.