The generator matrix

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

generates a code of length 32 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+584x^27+1947x^28+4634x^29+7922x^30+10452x^31+13876x^32+11622x^33+7878x^34+3992x^35+1789x^36+680x^37+118x^38+28x^39+3x^40+6x^41+2x^42+2x^45

The gray image is a code over GF(2) with n=256, k=16 and d=108.
This code was found by Heurico 1.16 in 15.2 seconds.