The generator matrix

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

generates a code of length 72 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+246x^65+342x^66+672x^67+627x^68+770x^69+717x^70+768x^71+505x^72+692x^73+528x^74+554x^75+379x^76+470x^77+276x^78+296x^79+142x^80+90x^81+54x^82+42x^83+10x^84+4x^85+3x^86+4x^87

The gray image is a code over GF(2) with n=288, k=13 and d=130.
This code was found by Heurico 1.16 in 10 seconds.