The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+89x^64+300x^65+470x^66+530x^67+502x^68+424x^69+480x^70+516x^71+392x^72+206x^73+100x^74+52x^75+7x^76+8x^77+4x^78+4x^79+4x^81+2x^83+1x^84+1x^86+2x^89+1x^94

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 0.453 seconds.