The generator matrix

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

generates a code of length 16 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+46x^11+120x^12+306x^13+479x^14+672x^15+843x^16+676x^17+501x^18+302x^19+92x^20+42x^21+9x^22+4x^23+3x^26

The gray image is a code over GF(2) with n=64, k=12 and d=22.
This code was found by Heurico 1.16 in 0.0961 seconds.