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

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+238x^58+456x^59+802x^60+856x^61+1226x^62+1228x^63+1425x^64+1340x^65+1478x^66+1392x^67+1486x^68+1104x^69+992x^70+828x^71+636x^72+332x^73+268x^74+128x^75+116x^76+16x^77+18x^78+14x^80+4x^82

The gray image is a code over GF(2) with n=264, k=14 and d=116.
This code was found by Heurico 1.13 in 4.64 seconds.