The generator matrix

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

generates a code of length 67 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+414x^61+1362x^62+1874x^63+3190x^64+3448x^65+4412x^66+3984x^67+4474x^68+3238x^69+2743x^70+1468x^71+1205x^72+508x^73+204x^74+128x^75+56x^76+24x^77+13x^78+18x^79+2x^80+2x^82

The gray image is a code over GF(2) with n=536, k=15 and d=244.
This code was found by Heurico 1.16 in 10.6 seconds.