The generator matrix

 1  0  0  0  1  1  1  0  X X+2  0  1  1  1  1  2 X+2 X+2  1  0  2  1  X X+2  1  1  1  1  1  1 X+2  1  1  1  0  1  1  1  2  0  1  1  1  1  0  1  X  X X+2 X+2  0  0 X+2  1  X  1  1  1  1  1  2  1  1  1  1  1  2  1  0  2  1  1
 0  1  0  0  X  0 X+2  X  1  1  1  3 X+1  1 X+3  2  1  2 X+2 X+2  1  1  1  1 X+2  1  0  2  0  1 X+2  3  3  1  1  1  X  2  1 X+2 X+3 X+2  3  3  1 X+2  X X+2  1  0  0  X  1 X+1  1  0 X+3 X+1  3  3  1 X+2 X+2 X+1  2  0  2  2  X  1  3  0
 0  0  1  0  X  1  3  1  1 X+2  3 X+1 X+2  1 X+2  1  2  X X+3  1 X+3  1  0 X+3  2  0  3  X  2  1  1  X X+1  X X+3 X+3  3 X+3  3  1  2  0  0  1  0 X+3 X+2  1  0  1  2  0 X+2 X+3  X X+1  2  1  3  X  1  2  X X+3  0  0  1 X+3  1  3  2  0
 0  0  0  1 X+1  1  0  1  2 X+1  1  0  1 X+3  0 X+2  3  1 X+1 X+3  1  2 X+2  2  X X+3 X+2 X+3  X  1 X+3  3 X+2  X X+1 X+1  X  1  X  1  1  1  0  1  1  2  1 X+2  X X+2  1  1 X+1 X+1  0  0  3  0 X+2  X  3  0  1  3  0  1  0  3  2 X+3 X+3  0
 0  0  0  0  2  0  2  2  2  2  0  0  0  2  2  0  2  0  0  2  0  0  0  2  0  2  2  0  2  2  0  2  2  0  2  0  0  2  0  0  0  2  2  0  2  2  2  2  0  2  0  0  0  2  0  2  2  0  0  0  2  0  0  2  2  0  0  0  0  2  2  0
 0  0  0  0  0  2  2  2  2  0  2  2  0  2  0  2  2  2  0  0  0  0  2  0  2  0  0  2  2  0  2  2  2  0  2  2  0  0  2  0  2  2  2  0  2  2  2  0  0  2  2  0  0  0  2  0  0  2  0  2  2  0  0  2  0  2  2  2  0  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+54x^63+354x^64+470x^65+775x^66+880x^67+1187x^68+1110x^69+1515x^70+1166x^71+1647x^72+1182x^73+1552x^74+950x^75+1010x^76+776x^77+801x^78+368x^79+248x^80+124x^81+82x^82+60x^83+30x^84+14x^85+8x^86+8x^87+2x^88+4x^89+3x^90+2x^91+1x^92

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 13 seconds.