The generator matrix

 1  0  1  1  1 X+2  X  1  1  2  1  1 3X+2  1 3X  1  1  1 2X  1  1  1  1 2X+2  1  1  1  1  1  1  1  1
 0  1 X+1 3X+2  3  1  1  2 3X+3  1 X+2 2X+3  1 3X  1  1 2X X+1  1 2X X+1 X+2 2X+3  1 2X+2  X 2X+2  X X+3 2X+1 3X+1  3
 0  0 2X+2  0  2 2X+2  2  0  2  0 2X+2 2X 2X 2X  0  2 2X+2 2X 2X+2  2 2X 2X+2  0 2X+2 2X+2 2X+2  2  2  0  0 2X+2 2X+2
 0  0  0 2X  0  0 2X  0 2X 2X  0  0 2X 2X  0 2X  0  0 2X  0 2X  0 2X  0 2X 2X 2X 2X  0 2X  0  0
 0  0  0  0 2X  0 2X 2X  0 2X 2X 2X  0 2X 2X 2X 2X 2X 2X  0 2X  0 2X  0 2X  0 2X  0  0  0 2X  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+144x^28+192x^29+640x^30+576x^31+1028x^32+576x^33+592x^34+192x^35+128x^36+16x^38+10x^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 0.109 seconds.