The generator matrix

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

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+110x^59+243x^60+566x^61+580x^62+992x^63+899x^64+1352x^65+1276x^66+1656x^67+1299x^68+1662x^69+1197x^70+1256x^71+921x^72+932x^73+435x^74+454x^75+180x^76+168x^77+91x^78+40x^79+35x^80+18x^81+1x^82+4x^83+6x^84+4x^85+4x^86+2x^89

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 12.9 seconds.