The generator matrix

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

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+212x^27+1112x^28+2074x^29+4115x^30+5256x^31+7338x^32+5234x^33+4211x^34+1886x^35+914x^36+286x^37+93x^38+20x^39+3x^40+6x^41+5x^42+2x^43

The gray image is a code over GF(2) with n=256, k=15 and d=108.
This code was found by Heurico 1.16 in 4.37 seconds.