The generator matrix

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

generates a code of length 67 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+132x^63+232x^64+252x^65+242x^66+340x^67+291x^68+220x^69+154x^70+136x^71+35x^72+8x^73+2x^74+1x^78+1x^92+1x^94

The gray image is a code over GF(2) with n=536, k=11 and d=252.
This code was found by Heurico 1.16 in 0.219 seconds.