The generator matrix

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

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+89x^64+212x^65+380x^66+484x^67+641x^68+664x^69+811x^70+772x^71+564x^72+728x^73+614x^74+548x^75+466x^76+376x^77+269x^78+220x^79+131x^80+68x^81+79x^82+24x^83+22x^84+20x^86+3x^88+3x^90+3x^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 3.52 seconds.