The generator matrix

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

generates a code of length 72 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+242x^65+1274x^66+2712x^67+4246x^68+5612x^69+6889x^70+7956x^71+8229x^72+8078x^73+7226x^74+5076x^75+3481x^76+2192x^77+1229x^78+620x^79+262x^80+116x^81+42x^82+36x^83+13x^84+4x^86

The gray image is a code over GF(2) with n=576, k=16 and d=260.
This code was found by Heurico 1.16 in 40.9 seconds.