The generator matrix

 1  0  0  1  1  1 X+2  1  1  0  X  1  1  X  1  1  X  X  1  1 X+2  1  1  X  1  2 X+2 X+2  1  1  1  0  0  1  1  0 X+2  1  1  1  X  1  1  1  1 X+2  0  1  1  0  1  1 X+2  1 X+2  2  1  1  X X+2  1 X+2  1  1 X+2  0  1  2  0  1  1  1
 0  1  0  0  1 X+1  1 X+2  3  1  X  3 X+2  1 X+3  0  2  1 X+1  X  1 X+3  0  1  1  1  1  1 X+2  1  3  2  1  X X+1  1 X+2 X+1 X+3  0  2 X+2  1  0 X+1  1  1 X+3  3  1  2  X  2 X+3  X  1  1  X  1  1 X+2  1  0  X  2  1 X+2  1  1 X+1  0  2
 0  0  1  1  1  0  1  1  3  3  1  0  2  X  1  X  1 X+2 X+2  1 X+3  0  2  0 X+3 X+3  3  X X+3 X+1  X  1 X+2  X  0  3  1 X+3  X X+1  1  1 X+2 X+3  1  1  1  X  2 X+3 X+2 X+2  1  X  1  X X+1  0  3 X+1  2  X  X X+2  1  X X+3  X  2 X+2 X+2  0
 0  0  0  X  0  0  2  2 X+2  X  X  X  X X+2 X+2  2  0  0  0  2  0  X  X X+2  2  0  X  2 X+2  2  0  X  X X+2  X X+2 X+2  0  X X+2  2  2  2  X X+2  2  X  2 X+2  X  2  0 X+2  X  X  2 X+2  2  X  X  X X+2  X X+2  X  0  2  X  X X+2  2  0
 0  0  0  0  X  2  X X+2  2  2 X+2 X+2  X X+2 X+2  X  X X+2 X+2  0  0  0  2  2  2 X+2  0  0 X+2  X  2  X  X  2 X+2  X  2  0  0  2  2  2 X+2 X+2  2  2 X+2  2  X  0  2  X  2 X+2  0 X+2  0  0  X  2  2  2  X  X X+2  0  X  0  2 X+2  0  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+68x^64+224x^65+413x^66+504x^67+683x^68+732x^69+593x^70+684x^71+675x^72+646x^73+668x^74+614x^75+510x^76+392x^77+270x^78+164x^79+130x^80+88x^81+58x^82+30x^83+7x^84+12x^85+11x^86+4x^87+4x^88+2x^89+3x^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 3.63 seconds.