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

generates a code of length 66 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+59x^54+84x^55+172x^56+278x^57+332x^58+430x^59+536x^60+770x^61+957x^62+1020x^63+1307x^64+1466x^65+1516x^66+1548x^67+1394x^68+1188x^69+823x^70+642x^71+510x^72+416x^73+310x^74+204x^75+142x^76+96x^77+78x^78+38x^79+34x^80+8x^81+18x^82+2x^83+2x^85+2x^86+1x^94

The gray image is a code over GF(2) with n=264, k=14 and d=108.
This code was found by Heurico 1.16 in 20.3 seconds.