The generator matrix

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

generates a code of length 71 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+596x^65+1251x^66+2278x^67+2759x^68+3636x^69+4094x^70+4546x^71+3570x^72+3340x^73+2651x^74+1946x^75+1044x^76+576x^77+165x^78+174x^79+57x^80+40x^81+14x^82+16x^83+9x^84+4x^85+1x^86

The gray image is a code over GF(2) with n=568, k=15 and d=260.
This code was found by Heurico 1.16 in 11.1 seconds.