The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+502x^27+2120x^28+4542x^29+7630x^30+11526x^31+12653x^32+11928x^33+7982x^34+4132x^35+1716x^36+614x^37+146x^38+30x^39+6x^40+4x^41+2x^42+2x^43

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 15.8 seconds.