The generator matrix

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

generates a code of length 32 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+52x^29+182x^30+236x^31+181x^32+148x^33+118x^34+68x^35+24x^36+8x^37+2x^40+2x^42+2x^46

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 0.031 seconds.