The generator matrix

 1  0  0  1  1  1  2  0  0  1  1  2  1  1  X X+2  1  0  1  1  1  2  1  0  1  1  2  1  0  X X+2  0 X+2  1  1  1  1 X+2  1  1  1 X+2 X+2  1  1 X+2  1 X+2  1  1  1  X  0  1  1  1  X  X  X  2  0  1  X  2  X X+2  1  1  0  2  1  1
 0  1  0  0  3  3  1 X+2  1  2  1  1  2  1  X  2  2  1  3  1  0  1  2  1  1  0  1  3 X+2 X+2  0  2 X+2 X+1 X+3 X+3 X+1  X X+1 X+3  X  1  1  X X+2  1 X+2  1 X+3 X+2 X+2  1  0  X X+1 X+2  1  0  1  X  2  X  1 X+2  2  0  0 X+2  1  1 X+2  X
 0  0  1 X+1 X+3  2 X+3  1 X+2 X+2  X  3  3  1  1  1 X+3  2  3  0  X  3  2  X X+1  1 X+3 X+2  1  1  1  1  1 X+1 X+1  1  1  1  0  0  X X+1  3  2  X X+3  2  1  X X+1  1  X  1 X+1  X  3  0  1  0  1  1  3  X  1  1  1 X+2  2  3 X+1  3  X
 0  0  0  2  2  0  2  2  2  2  2  0  0  0  0  2  0  2  2  2  0  2  2  0  0  2  0  0  0  2  0  2  0  0  2  2  0  2  0  2  0  2  0  0  2  0  2  2  2  2  0  2  2  0  0  2  0  0  2  0  0  0  0  2  2  2  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+95x^68+136x^69+184x^70+188x^71+94x^72+80x^73+41x^74+40x^75+12x^76+40x^77+49x^78+28x^79+12x^80+4x^82+16x^84+1x^86+1x^88+1x^90+1x^92

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 0.218 seconds.