The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 2X  1  1  1  1  1
 0  X  2 3X+2  0 3X+2  2 3X  0 3X+2  2 3X  0 3X+2  2 3X 2X X+2 2X+2 3X  0 3X+2  2 3X+2 X+2 3X 2X  2 2X+2  0 2X  0
 0  0 2X  0  0  0  0 2X  0 2X 2X  0 2X 2X 2X 2X 2X 2X 2X  0 2X  0  0 2X  0 2X 2X  0 2X 2X 2X  0
 0  0  0 2X  0  0 2X  0 2X 2X 2X 2X 2X 2X  0  0  0  0 2X  0 2X  0  0  0 2X 2X 2X 2X 2X  0  0  0
 0  0  0  0 2X 2X 2X 2X  0  0  0 2X 2X 2X 2X  0  0  0 2X 2X  0  0  0 2X 2X  0 2X  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+26x^28+60x^29+31x^30+404x^31+27x^32+388x^33+16x^34+12x^35+10x^36+32x^37+16x^38+1x^62

The gray image is a code over GF(2) with n=256, k=10 and d=112.
This code was found by Heurico 1.16 in 0.032 seconds.