The generator matrix

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

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+101x^28+346x^29+597x^30+752x^31+640x^32+714x^33+505x^34+242x^35+119x^36+28x^37+16x^38+30x^39+3x^40+1x^42+1x^46

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 0.11 seconds.