The generator matrix

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

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+78x^64+160x^66+253x^68+400x^70+380x^72+313x^74+232x^76+106x^78+56x^80+36x^82+19x^84+6x^86+4x^88+3x^90+1x^112

The gray image is a code over GF(2) with n=288, k=11 and d=128.
This code was found by Heurico 1.16 in 0.585 seconds.