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

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+62x^56+124x^57+181x^58+286x^59+329x^60+388x^61+475x^62+566x^63+621x^64+706x^65+778x^66+722x^67+684x^68+578x^69+463x^70+346x^71+238x^72+194x^73+138x^74+104x^75+55x^76+50x^77+37x^78+24x^79+26x^80+8x^81+7x^82+1x^94

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 5.78 seconds.