The generator matrix

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

generates a code of length 72 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+207x^64+24x^65+342x^66+108x^67+389x^68+152x^69+486x^70+244x^71+435x^72+188x^73+376x^74+200x^75+335x^76+80x^77+192x^78+20x^79+144x^80+4x^81+84x^82+4x^83+51x^84+22x^86+4x^88+2x^90+1x^96+1x^100

The gray image is a code over GF(2) with n=288, k=12 and d=128.
This code was found by Heurico 1.16 in 97.4 seconds.