The generator matrix

 1  0  1  1  1 3X+2  1  1  2  1  1 3X  1  1  1  1  0 3X+2  1  1  1  1  0 3X+2  1  1  1  1  1  1  1  1
 0  1 X+1 3X+2 2X+3  1  2 X+3  1 3X 2X+1  1  0 3X+2 X+1 2X+3  1  1  2 3X X+3 2X+3  1  1  0 3X+2  2 2X+2 X+2 X+1 2X  0
 0  0 2X  0 2X  0 2X  0 2X 2X  0 2X  0  0  0  0 2X 2X 2X 2X 2X 2X  0  0 2X 2X  0  0 2X  0 2X  0
 0  0  0 2X 2X 2X 2X  0  0  0 2X 2X 2X  0 2X  0 2X  0  0 2X 2X  0 2X  0 2X  0  0 2X 2X  0  0  0

generates a code of length 32 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+64x^29+155x^30+240x^31+102x^32+240x^33+156x^34+64x^35+1x^46+1x^48

The gray image is a code over GF(2) with n=256, k=10 and d=116.
This code was found by Heurico 1.16 in 0.015 seconds.