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

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+284x^65+338x^66+676x^67+493x^68+922x^69+570x^70+822x^71+445x^72+792x^73+485x^74+708x^75+327x^76+460x^77+271x^78+268x^79+74x^80+124x^81+57x^82+48x^83+4x^84+10x^85+7x^86+6x^87

The gray image is a code over GF(2) with n=288, k=13 and d=130.
This code was found by Heurico 1.13 in 22.9 seconds.