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

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+25x^64+64x^65+109x^66+126x^67+119x^68+176x^69+172x^70+174x^71+217x^72+190x^73+155x^74+146x^75+100x^76+48x^77+52x^78+46x^79+41x^80+24x^81+22x^82+16x^83+8x^84+8x^85+4x^87+2x^89+1x^90+1x^92+1x^114

The gray image is a code over GF(2) with n=288, k=11 and d=128.
This code was found by Heurico 1.16 in 0.491 seconds.