The generator matrix

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

generates a code of length 72 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+357x^68+335x^72+308x^76+15x^80+6x^84+1x^88+1x^132

The gray image is a code over GF(2) with n=288, k=10 and d=136.
This code was found by Heurico 1.16 in 6.94 seconds.