The generator matrix

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

generates a code of length 29 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+69x^24+460x^25+1156x^26+2116x^27+2488x^28+3722x^29+2779x^30+2060x^31+910x^32+454x^33+122x^34+16x^35+18x^36+2x^37+7x^38+2x^40+2x^41

The gray image is a code over GF(2) with n=232, k=14 and d=96.
This code was found by Heurico 1.16 in 0.938 seconds.