The generator matrix

 1  0  1  1  1 X+2  1  1  2  1  X  1  2  1  1  1  X  1  X  1  1  1  1  2  1  0  1  1 X+2  1  1  2  1  1  1  0  1  1  2  1  1  1  X  1 X+2  1  1  1  2  1  1  X  1  1  1  1  1  1  1  2  1  0  0  2  1  1
 0  1  1  0  1  1  X X+3  1 X+2  1 X+3  1  0 X+1 X+2  1  3  1  2 X+1  3  X  1  2  1 X+3 X+2  1 X+2 X+1  1 X+1  2  1  1 X+3 X+1  1  3  0  2  1  X  1 X+1  3  2  1  3  0  1 X+3  0  0  0 X+1  1  3  1  X  2  X  0  2 X+3
 0  0  X  0  0  0  0  0  0  2  2 X+2  X  X  2  X X+2  X X+2  X  X  0 X+2 X+2  2  0  X  X  0  2  2 X+2  2  0  2  2  X  0  0 X+2  2  X  0  0  2  2 X+2 X+2  X  X X+2  X  0  0 X+2  X  0 X+2  0  0  0  X  X  2  X  X
 0  0  0  X  0  0  X  2  X  2 X+2  2 X+2  2  X  0  X X+2  0  X  X X+2 X+2  0  X  0 X+2  X  X  2  0  2 X+2  X  X  X  X  0  0  X  2  2  2  X  0 X+2  0  0  0  2  0 X+2 X+2 X+2  0  X  X  2  0  2  0 X+2 X+2  X  0  2
 0  0  0  0  X  0  0 X+2  2  0  2  2 X+2  X X+2  X  X  2  X  X  0  X  X X+2  0  2 X+2  0  X  X  0  0  2  X  2  X  X X+2 X+2  X X+2  X X+2  0  X  X  X  2  2 X+2  2  2 X+2 X+2  X  2  X  0  0  2  2  0 X+2  0  X  0
 0  0  0  0  0  2  0  0  2  0  2  0  2  0  0  0  2  0  2  0  2  2  2  0  2  0  0  0  2  2  0  0  2  0  0  0  2  2  2  0  0  2  0  2  2  0  2  2  2  0  2  2  2  0  2  0  2  2  0  2  2  2  2  0  2  0
 0  0  0  0  0  0  2  2  0  2  2  2  2  0  0  2  0  2  2  2  2  0  2  2  2  2  2  0  0  0  2  0  0  0  2  2  0  2  2  0  2  2  2  0  0  2  2  2  2  0  0  2  2  2  0  0  0  0  2  0  2  2  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+77x^56+160x^57+276x^58+426x^59+615x^60+746x^61+910x^62+1200x^63+1423x^64+1652x^65+1655x^66+1544x^67+1382x^68+1148x^69+989x^70+758x^71+473x^72+332x^73+223x^74+140x^75+107x^76+50x^77+36x^78+26x^79+18x^80+8x^81+5x^82+2x^83+1x^86+1x^90

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 15 seconds.