The generator matrix

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

generates a code of length 66 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+282x^58+396x^59+832x^60+836x^61+1268x^62+1076x^63+1511x^64+1384x^65+1616x^66+1184x^67+1461x^68+1116x^69+1144x^70+724x^71+671x^72+352x^73+288x^74+76x^75+83x^76+24x^77+40x^78+17x^80+2x^82

The gray image is a code over GF(2) with n=264, k=14 and d=116.
This code was found by Heurico 1.16 in 12.2 seconds.