The generator matrix

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

generates a code of length 69 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+454x^63+1448x^64+2056x^65+2814x^66+3878x^67+3953x^68+4132x^69+4005x^70+3508x^71+2680x^72+1818x^73+1005x^74+538x^75+280x^76+72x^77+55x^78+38x^79+12x^80+16x^81+1x^82+1x^84+1x^88+2x^89

The gray image is a code over GF(2) with n=552, k=15 and d=252.
This code was found by Heurico 1.16 in 10.5 seconds.