The generator matrix

 1  0  0  1  1  1  0  2  0 X^2  1  1  1  1 X+2  1 X+2  1  1  1 X^2+X+2 X^2+X X^2+X+2  X  1  1  1  1  1  1 X^2+2  1  1  X  1  1 X^2+X X^2+2  1  1 X^2+X+2 X^2+X+2  1  1 X^2+X+2 X^2+X+2  1  2  1  1 X^2+2 X+2  1  2  1  1 X^2+2  X  1  1  2  1  1  1  1  0  1 X+2 X^2+2  1  1
 0  1  0  0 X^2+1 X^2+3  1 X^2+X  1  1  2  0  3  3 X^2+X+2  X  1  X X+1 X^2+X+1  1 X^2  1  1 X^2+X+3 X^2+X X^2 X^2+X+3  2 X^2+X+2  1 X^2+X  0  1 X^2+1 X^2+1  1 X^2+2 X^2+2 X+3 X+2 X^2+2 X^2+X+1  1  1 X^2 X^2+X+2 X^2  2 X+2 X^2+X  1  3  1 X+2 X^2+X  1  1  X X^2+X+3  1 X+3 X^2+2 X^2+X+2  0  X  X  1 X^2+X+2 X^2+X+2  0
 0  0  1 X+1 X^2+X+1 X^2 X^2+X+1  1 X^2+X+2  1 X^2+X X^2+1  X X^2+1  1 X^2+X+1 X+2 X+2  2 X+3 X^2+1  1  2 X+3 X+2  3  0  1 X+2 X+3 X^2  0  1 X^2+X+1 X^2+X+2 X+1  1  1 X^2+X+2 X^2+3  1  1 X+2 X^2  0  1 X^2+X+3  1  2  0  1  1 X^2+3 X+2 X^2+X+2  3 X^2+3 X^2+X+2  1 X^2+2  2 X^2+2 X^2+X+3  1 X^2+X+3  1 X^2 X^2+X+2  1  2  0
 0  0  0 X^2 X^2  0 X^2 X^2 X^2+2  0 X^2+2  2 X^2  0 X^2  2 X^2+2 X^2+2  0  2 X^2  2  2  0  0  2 X^2+2 X^2+2  2 X^2  2 X^2 X^2 X^2+2 X^2+2  2  0  0  0 X^2  2 X^2 X^2 X^2+2 X^2 X^2+2 X^2+2 X^2 X^2 X^2+2  0 X^2+2 X^2+2 X^2  0 X^2  2  2  0  0 X^2+2 X^2+2  0 X^2+2  2  2  0 X^2+2 X^2  2  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+138x^65+623x^66+1042x^67+1800x^68+1682x^69+2395x^70+1790x^71+2057x^72+1562x^73+1412x^74+734x^75+548x^76+270x^77+189x^78+58x^79+40x^80+12x^81+19x^82+8x^83+2x^84+2x^86

The gray image is a code over GF(2) with n=568, k=14 and d=260.
This code was found by Heurico 1.16 in 3.02 seconds.