The generator matrix

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

generates a code of length 66 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+146x^56+28x^57+422x^58+184x^59+729x^60+556x^61+1330x^62+1036x^63+1602x^64+1248x^65+1886x^66+1328x^67+1707x^68+988x^69+1100x^70+556x^71+730x^72+188x^73+320x^74+32x^75+142x^76+86x^78+24x^80+8x^82+6x^84+1x^88

The gray image is a code over GF(2) with n=264, k=14 and d=112.
This code was found by Heurico 1.16 in 16 seconds.