The generator matrix

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

generates a code of length 69 over Z4[X]/(X^2+2) 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 0.531 seconds.