The generator matrix

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

generates a code of length 69 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+272x^60+636x^61+1016x^62+1368x^63+1802x^64+1976x^65+2382x^66+2700x^67+2764x^68+3000x^69+2804x^70+2848x^71+2365x^72+1992x^73+1686x^74+1184x^75+863x^76+540x^77+312x^78+88x^79+86x^80+48x^81+24x^82+4x^83+5x^84+2x^88

The gray image is a code over GF(2) with n=276, k=15 and d=120.
This code was found by Heurico 1.13 in 17 seconds.