The generator matrix

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

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+500x^64+1474x^66+2435x^68+2584x^70+2895x^72+2338x^74+2118x^76+1178x^78+627x^80+156x^82+51x^84+14x^86+9x^88+4x^92

The gray image is a code over GF(2) with n=288, k=14 and d=128.
This code was found by Heurico 1.13 in 90.7 seconds.