The generator matrix

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

generates a code of length 69 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+707x^64+920x^65+2036x^66+1528x^67+2666x^68+1672x^69+2094x^70+1424x^71+1523x^72+648x^73+644x^74+184x^75+220x^76+24x^77+54x^78+28x^80+4x^82+6x^84+1x^88

The gray image is a code over GF(2) with n=552, k=14 and d=256.
This code was found by Heurico 1.16 in 385 seconds.