The generator matrix

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

generates a code of length 69 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+172x^63+333x^64+370x^65+414x^66+374x^67+422x^68+400x^69+255x^70+286x^71+269x^72+190x^73+184x^74+142x^75+106x^76+64x^77+35x^78+30x^79+19x^80+12x^81+4x^82+4x^83+2x^84+4x^85+4x^86

The gray image is a code over GF(2) with n=276, k=12 and d=126.
This code was found by Heurico 1.11 in 0.398 seconds.