The generator matrix

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

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+102x^61+529x^62+1180x^63+1660x^64+1938x^65+2103x^66+2090x^67+1850x^68+1872x^69+1119x^70+814x^71+588x^72+242x^73+157x^74+50x^75+47x^76+22x^77+4x^78+6x^79+5x^80+4x^83+1x^84

The gray image is a code over GF(2) with n=536, k=14 and d=244.
This code was found by Heurico 1.16 in 2.92 seconds.