The generator matrix

 1  0  1  1  1 X^2+X+2  1  X  1  2  1  1 X^2  1  1  1 X^2+X  1  1 X^2+2  1 X+2  1  1  1  1  1 X+2  1  0  1  1  1  1  1  2 X^2+X+2  1  1  1  1  1  2  X X^2  1  1 X^2+X  1  1  X  1  1  1  1  1  1  1  1  1  1  1  X  X  1 X^2  1  1  1
 0  1 X+1 X^2+X X^2+3  1 X^2+2  1 X^2+X+1  1 X+2  1  1  2 X+1 X^2+X+2  1 X^2+X+3 X^2  1  X  1 X+1 X^2+X+3 X^2+1  3  0  1 X^2+1  1 X^2+X+2 X+3 X^2 X^2+3 X^2+X  1  1  3 X^2+2 X+2 X^2+X X+3  1  1  1  2  1  1  0  X X^2 X+2  2 X^2 X^2+2 X+2  X X^2 X^2 X+2 X^2+X X^2+X+2 X^2+X X^2+2  2  1 X^2+3 X^2+1  2
 0  0 X^2  0 X^2+2 X^2  0 X^2 X^2+2 X^2+2  0 X^2 X^2+2 X^2  2 X^2+2  0  2 X^2  0 X^2+2  0  2  2  0  2  0  0  2  0 X^2+2 X^2 X^2 X^2+2  2 X^2 X^2  0  0  2 X^2 X^2  2 X^2 X^2 X^2+2 X^2+2  2 X^2+2 X^2+2  2 X^2 X^2  0  2  0  0  2  0 X^2  2  2 X^2 X^2  2 X^2  2  0  0
 0  0  0  2  0  0  0  0  2  2  2  2  2  0  2  2  2  0  2  2  0  0  2  0  0  2  2  0  2  0  2  0  2  0  0  0  2  0  2  0  0  2  2  2  0  0  2  2  2  2  0  0  0  2  2  0  2  0  0  2  0  2  0  2  0  2  0  0  2
 0  0  0  0  2  0  2  2  0  0  2  2  2  2  0  2  0  0  0  2  0  2  2  2  0  2  2  0  0  2  0  2  2  0  2  0  2  2  0  0  2  2  0  0  2  0  0  2  2  0  2  2  0  2  2  0  0  0  0  2  0  0  0  0  2  0  0  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+108x^64+274x^65+378x^66+558x^67+551x^68+594x^69+410x^70+466x^71+332x^72+244x^73+93x^74+26x^75+29x^76+6x^77+12x^78+2x^79+2x^81+2x^82+4x^83+2x^84+1x^96+1x^98

The gray image is a code over GF(2) with n=552, k=12 and d=256.
This code was found by Heurico 1.16 in 0.532 seconds.