The generator matrix

 1  0  0  0  0  1  1  1  2  1  1  1  1 X+2  0 X+2  1  2  1  1  1  0 X+2 X+2  1  0  X  1  1  1  0  2 X+2  X  1  1  1  2  1 X+2  0  0  1  1  X  0  1  X  0  X  1  1  1  1  1  2  1  1  1  1  1  1  1  1  X  1
 0  1  0  0  0  0  0  0  0  2  2  2  2  0  0  2  2  1  3 X+1 X+3  1  1  1 X+3  1  1  3  1  3  1 X+2  X  1  X X+2  X  1 X+3  1 X+2  X  2 X+1  1  X X+3 X+2  1  1 X+2  X X+2  0 X+3 X+2  0  X X+3  3 X+1  0  1  3  X  X
 0  0  1  0  0  2  1  3  1  X  0 X+1 X+3  1  1 X+2 X+3 X+3 X+2 X+2 X+1  3  0 X+3 X+3  X X+3 X+2  2  3  2  2  1  2  0  1  1 X+1 X+3  3  1 X+2  3  X  2  0 X+2  1  3  X  X X+3  3  X  1 X+2 X+1  X  2  X  1  0  0 X+2  X  0
 0  0  0  1  0  3  1  2  3  0 X+1  X  3  0 X+3  1 X+3  3 X+2 X+1 X+1  2  1  X  1 X+2  1  2 X+1  2 X+1  X X+3  X  2 X+3 X+2  2  2  3  2  1 X+2  1 X+1  1  1 X+2  X  X  1  0  2  3  2  1  2 X+2  2  0  1 X+1 X+1  3  1  2
 0  0  0  0  1  1  2  3  3 X+1  X  0  3 X+3  X X+1 X+3  1 X+3 X+1  1 X+2  3 X+1  0  1  X X+2  0 X+3 X+2  1 X+3  2 X+3  X  1 X+2 X+2 X+2 X+1  0  2  1 X+2  3  2  2 X+1 X+3  3 X+2  0  3  2 X+3  3 X+1  1  0  1  0  1 X+2  3 X+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+182x^57+610x^58+942x^59+1392x^60+1698x^61+2200x^62+2488x^63+2475x^64+2892x^65+2924x^66+2960x^67+2760x^68+2524x^69+2176x^70+1614x^71+1194x^72+712x^73+488x^74+310x^75+134x^76+54x^77+14x^78+6x^79+10x^80+2x^81+2x^82+2x^84+2x^86

The gray image is a code over GF(2) with n=264, k=15 and d=114.
This code was found by Heurico 1.13 in 16.1 seconds.