The generator matrix

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

generates a code of length 67 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+238x^62+280x^63+440x^64+312x^65+676x^66+400x^67+561x^68+272x^69+393x^70+216x^71+163x^72+56x^73+68x^74+19x^76+1x^118

The gray image is a code over GF(2) with n=536, k=12 and d=248.
This code was found by Heurico 1.16 in 1.33 seconds.