The generator matrix

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

generates a code of length 66 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+78x^57+224x^58+448x^59+752x^60+910x^61+1066x^62+1256x^63+1207x^64+1448x^65+1596x^66+1504x^67+1457x^68+1188x^69+1094x^70+812x^71+476x^72+330x^73+212x^74+156x^75+64x^76+38x^77+28x^78+12x^79+8x^80+8x^81+4x^82+4x^83+3x^84

The gray image is a code over GF(2) with n=264, k=14 and d=114.
This code was found by Heurico 1.16 in 12.4 seconds.