The generator matrix

 1  0  1  1  1 X+2  1  1  2  1 3X+2  1  1 X+2  1 2X  1  1  1  1 2X 2X+2  1  1 3X 2X+2 X+2  1 2X 3X  1  X
 0  1 X+1 X+2 2X+3  1 3X+1  2  1 3X+2  1 2X+3 2X  1 X+1  1  3 X+2 X+3  1  1  1 3X+2 3X+2  1  X  1  X  1  1 2X X+2
 0  0 2X+2  0  0 2X  0 2X 2X  2  2  2 2X+2  2  0  2 2X+2  2 2X+2 2X 2X 2X+2  0 2X+2 2X  2  0  2  0 2X  0  0
 0  0  0  2 2X 2X+2 2X+2  0  0 2X+2 2X+2  2 2X 2X 2X 2X  0 2X  2 2X+2  2  2 2X+2  2  0  0  0 2X 2X 2X 2X+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+133x^28+272x^29+534x^30+752x^31+775x^32+752x^33+456x^34+272x^35+106x^36+32x^38+8x^40+1x^44+2x^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.