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 2X+2  1  1  1  1  1  1  1
 0  2  0  2  0  2 2X 2X+2  0  2  0  2  0 2X+2 2X  2 2X+2 2X 2X  2  2 2X+2  0  0 2X  0  0 2X 2X  2 2X+2  0
 0  0 2X  0  0  0 2X  0  0  0 2X 2X  0 2X 2X  0 2X 2X  0 2X 2X 2X  0 2X  0  0 2X 2X  0  0  0  0
 0  0  0 2X  0  0  0 2X  0  0 2X 2X 2X 2X  0  0 2X  0  0 2X  0  0 2X 2X  0 2X 2X 2X 2X 2X 2X  0
 0  0  0  0 2X  0 2X  0  0 2X  0 2X 2X  0 2X 2X  0  0 2X 2X 2X 2X  0 2X  0 2X  0 2X  0 2X 2X  0
 0  0  0  0  0 2X  0 2X 2X 2X  0  0 2X 2X 2X  0  0 2X 2X 2X  0 2X 2X  0  0  0 2X 2X  0  0  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+36x^28+24x^29+27x^30+192x^31+527x^32+144x^33+16x^34+12x^36+24x^37+20x^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 0.031 seconds.