The generator matrix

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

generates a code of length 32 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+204x^29+1020x^30+520x^31+921x^32+320x^33+736x^34+184x^35+116x^36+52x^37+20x^38+2x^40

The gray image is a code over GF(2) with n=256, k=12 and d=116.
This code was found by Heurico 1.16 in 0.078 seconds.