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  0  X  1  1  1  1  X  1  2  1  0  1  2  1  1  0  X  1  2  0  1  1  X  1  X  X  X  0  X  1  0  1  2  0  1  1  2
 0  X  0  0  0  X X+2  X  0  2  2  0  X X+2  X X+2 X+2 X+2 X+2  2  0  0 X+2  2  0  2  X  X X+2  2 X+2 X+2  X  2  2  X  X  0  X  X  0 X+2  0  X  X  0  X  X  2  0  0 X+2  X  0  X X+2 X+2 X+2 X+2  X  2  2  0 X+2 X+2  0  2  0  2 X+2  2  2
 0  0  X  0  X  X X+2  0  0  0 X+2 X+2  X  X  2  0  X  2  0 X+2 X+2  2 X+2  2 X+2  0  2  2 X+2 X+2  0  0 X+2  2  0 X+2  2 X+2 X+2  2  0  X  X  2  2  X X+2  2  X  0  0 X+2  0  0  0  2  X  0  2  0 X+2  X  X  0  2  X  X  0  0  0 X+2  2
 0  0  0  X  X  0 X+2  X  2 X+2  X  2  2  X  X  2  0 X+2  0  X  2  X  X  0  2  X  0 X+2  X  X X+2 X+2  2  0  0  X  X  X  0 X+2  X X+2 X+2 X+2  X  0  X  X  2 X+2  X  X  2  X  2 X+2  0 X+2  X  0  2  0 X+2  2  2  0 X+2  X  X  2  0  0
 0  0  0  0  2  0  0  0  2  0  0  0  0  0  0  2  2  2  2  2  0  2  2  0  2  0  2  2  0  0  0  2  2  0  0  2  0  0  0  0  2  2  2  2  2  2  0  2  2  0  2  2  0  2  2  0  0  0  2  0  0  2  2  0  2  0  0  0  2  0  0  0
 0  0  0  0  0  2  0  2  0  0  2  2  0  2  2  0  0  0  2  2  2  0  0  2  2  2  0  0  0  0  0  2  2  0  2  0  0  2  0  0  2  0  2  0  2  2  2  2  2  2  0  2  2  2  2  2  2  0  0  2  2  2  2  2  0  0  0  2  0  2  0  2
 0  0  0  0  0  0  2  2  2  2  0  0  2  0  0  0  0  0  2  0  2  0  2  2  2  2  2  2  0  0  0  0  2  2  0  0  2  2  0  2  2  2  2  0  2  0  2  0  0  0  2  0  0  0  0  2  2  2  2  2  2  2  2  2  0  2  2  2  0  2  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+300x^64+212x^66+663x^68+552x^70+822x^72+512x^74+480x^76+208x^78+231x^80+28x^82+47x^84+24x^86+13x^88+2x^92+1x^104

The gray image is a code over GF(2) with n=288, k=12 and d=128.
This code was found by Heurico 1.16 in 77.9 seconds.