The generator matrix

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

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+113x^56+8x^57+370x^58+48x^59+552x^60+176x^61+712x^62+300x^63+901x^64+464x^65+982x^66+508x^67+918x^68+336x^69+604x^70+164x^71+453x^72+40x^73+276x^74+4x^75+165x^76+58x^78+28x^80+4x^82+4x^84+2x^86+1x^92

The gray image is a code over GF(2) with n=264, k=13 and d=112.
This code was found by Heurico 1.16 in 5.8 seconds.