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

generates a code of length 32 over Z4[X]/(X^3+2,2X) 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 0.031 seconds.