The generator matrix

 1  0  1  1  1 X+2  1  1  X  1  1  X  X  1  1  2  1  1  1  1  0  1  1  0  1  1  0  1 X+2  1  1  1  2  1  1  0  1  0  1 X+2  1  1 X+2  1  1  1 X+2  1  1  X  1  1  1  1  1  1  1  1  1  1  1  X  1  1  X  2  1  1  X  0  1  1
 0  1  1 X+2 X+1  1  3  2  1  X X+3  1  1  0 X+3  1  0 X+3  X  3  1  X  3  1  0 X+1  1 X+2  1 X+1 X+1  0  1 X+2  1  1  3  1  1  1  2 X+2  1  1 X+2 X+1  1 X+2  0  2  0  X  2  X  0  X  0  2  X X+2  2  X  2  3  1  X  0  X  X  1  0  1
 0  0  X  0  0  2  0 X+2  X X+2  X X+2  2  2  X  X X+2  2 X+2  X X+2  2  2  0  0  0  0  2  2  2  X X+2 X+2 X+2  X  X  0  0  2  2 X+2  0  X  X X+2  X X+2  2  2  0  0  X X+2  X X+2  0  2  2  0 X+2  X  0  0 X+2 X+2  2  X X+2  X  2  X  0
 0  0  0  2  0  2  2  2  2  0  2  0  0  2  2  2  0  0  2  0  0  0  2  2  0  2  0  0  0  2  2  2  0  2  2  0  0  2  0  2  0  2  2  0  0  0  2  2  0  2  2  0  2  2  0  0  2  2  0  0  0  2  0  2  0  2  0  0  2  2  2  0
 0  0  0  0  2  2  2  2  0  2  0  0  2  2  2  2  0  0  0  2  2  2  0  0  2  0  2  0  0  2  0  2  2  0  2  0  0  2  2  0  0  2  0  2  2  0  2  0  2  2  0  0  0  2  2  2  0  2  0  0  2  0  0  0  2  0  2  0  2  0  2  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+207x^68+248x^70+219x^72+160x^74+123x^76+40x^78+16x^80+4x^88+4x^96+2x^100

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 44.4 seconds.