The generator matrix

 1  0  0  1  1  1  X  1 X+2  1  1  X  1 X+2  1  X  2  1  1  X  1  1  0  0  1  1  1  2  2  1  1 X+2  X  1  1  0  1  1  1 X+2  1  0  2  1  2 X+2  1 X+2 X+2  1 X+2  1  X  X  1  1  1  0  1  1 X+2  1  1  1  1 X+2 X+2  2  1  1  1  1
 0  1  0  0  1 X+3  1  2  0  2 X+3  1 X+1  1  1 X+2  1  X  X  1  X  3  X  1 X+1  1  2  1  1 X+3 X+3  1  0  X  2  2  2 X+1 X+2  1 X+3  1  1 X+1  1  1  X X+2  1 X+2  0 X+2  1  1 X+1  3  0  1  0  1  0 X+3  X  3 X+2  X  1  1 X+2  3  X  0
 0  0  1  1 X+1  0  1 X+1  1  X X+1  X  X X+1  3  1  X X+2  0  2 X+1 X+2  1 X+1  0  1  1  1  0  2  3 X+3  1  1 X+2  1 X+3  X X+3 X+2 X+3  1  X  2 X+3  X  0  1  1  1  1  2 X+1  0  3  X X+3  0 X+3  0  1  X  3  1 X+2  1  X  X  3 X+3  2  0
 0  0  0  X  X X+2  2 X+2  0  0  X  2  X  0 X+2  0  0  2  2  2 X+2  X  0  2 X+2  0  0  X X+2  2  2  X X+2  0 X+2 X+2  X  0  2  X  0 X+2  2  X  0 X+2  2  X  X X+2  2  X  X  0  X  2  0 X+2 X+2  2  X X+2  X  2  X  X  0  X X+2  2  0  0
 0  0  0  0  2  0  0  2  2  2  0  2  2  0  0  2  0  0  2  2  0  0  0  2  2  2  0  2  0  2  0  2  0  0  2  0  2  2  2  2  2  2  2  0  2  2  2  2  2  2  2  0  0  0  2  0  0  2  0  0  2  0  0  0  2  0  2  0  2  2  2  0
 0  0  0  0  0  2  2  0  0  0  0  0  0  0  2  2  2  2  2  2  2  0  2  0  2  2  2  0  2  0  0  2  2  0  2  0  2  2  0  0  0  0  2  2  2  2  0  0  2  0  2  0  2  0  2  0  2  2  2  2  2  2  0  2  0  2  0  2  2  2  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+112x^64+168x^65+443x^66+470x^67+803x^68+474x^69+836x^70+528x^71+944x^72+438x^73+772x^74+422x^75+615x^76+308x^77+316x^78+152x^79+164x^80+66x^81+79x^82+24x^83+8x^84+14x^85+16x^86+4x^87+7x^88+4x^89+2x^90+2x^92

The gray image is a code over GF(2) with n=288, k=13 and d=128.
This code was found by Heurico 1.16 in 3.73 seconds.