The generator matrix

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

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+115x^28+820x^29+937x^30+1554x^31+1509x^32+1556x^33+780x^34+634x^35+143x^36+102x^37+26x^38+4x^39+8x^40+2x^41+1x^46

The gray image is a code over GF(2) with n=256, k=13 and d=112.
This code was found by Heurico 1.16 in 0.282 seconds.