The generator matrix

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

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+186x^63+283x^64+450x^65+390x^66+440x^67+323x^68+386x^69+256x^70+276x^71+219x^72+264x^73+168x^74+188x^75+107x^76+72x^77+24x^78+26x^79+9x^80+6x^81+10x^82+4x^83+2x^84+6x^85

The gray image is a code over GF(2) with n=276, k=12 and d=126.
This code was found by Heurico 1.16 in 74.5 seconds.