The generator matrix

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

generates a code of length 72 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+60x^63+284x^64+498x^65+799x^66+950x^67+1107x^68+1310x^69+1304x^70+1332x^71+1376x^72+1400x^73+1264x^74+1246x^75+998x^76+766x^77+605x^78+390x^79+309x^80+172x^81+116x^82+52x^83+15x^84+12x^85+7x^86+2x^87+6x^88+2x^89+1x^90

The gray image is a code over GF(2) with n=288, k=14 and d=126.
This code was found by Heurico 1.16 in 12.7 seconds.