The generator matrix

 1  0  1  1  1 3X+2  1  1  1  2  1 3X  1  1  1  0  1  1 3X+2  1  1  1  1  1  1  X  2  1  1  2  1  1
 0  1 X+1 3X+2 2X+3  1 X+3 2X+1  2  1 3X  1 2X+3 X+1  0  1 X+3 3X+2  1 2X+3 X+3 2X+1  0 3X 3X  2  1 X+1 3X  X 3X+2  0
 0  0 2X  0  0  0 2X  0 2X 2X 2X 2X 2X  0  0  0 2X  0  0 2X  0 2X 2X  0 2X  0 2X  0  0  0 2X  0
 0  0  0 2X  0 2X 2X 2X 2X 2X  0  0  0  0 2X 2X  0  0  0 2X 2X 2X  0  0 2X  0 2X 2X 2X 2X 2X  0
 0  0  0  0 2X  0 2X 2X  0  0  0  0 2X 2X  0  0 2X  0  0 2X 2X  0  0 2X 2X 2X 2X  0 2X 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+60x^28+152x^29+285x^30+296x^31+415x^32+408x^33+251x^34+88x^35+68x^36+16x^37+6x^38+1x^46+1x^50

The gray image is a code over GF(2) with n=256, k=11 and d=112.
This code was found by Heurico 1.16 in 0.046 seconds.