The generator matrix

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

generates a code of length 32 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+282x^28+40x^29+798x^30+488x^31+1060x^32+440x^33+564x^34+56x^35+306x^36+46x^38+14x^40+1x^48

The gray image is a code over GF(2) with n=256, k=12 and d=112.
This code was found by Heurico 1.16 in 2.97 seconds.