The generator matrix

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

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+130x^58+24x^59+428x^60+240x^61+833x^62+568x^63+1257x^64+976x^65+1612x^66+1196x^67+1834x^68+1336x^69+1707x^70+996x^71+1136x^72+608x^73+649x^74+156x^75+378x^76+40x^77+158x^78+4x^79+63x^80+29x^82+19x^84+2x^86+3x^88+1x^92

The gray image is a code over GF(2) with n=272, k=14 and d=116.
This code was found by Heurico 1.16 in 15.5 seconds.