The generator matrix

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

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+140x^24+840x^25+2144x^26+4104x^27+5512x^28+7048x^29+6066x^30+4072x^31+1765x^32+784x^33+204x^34+48x^35+36x^36+2x^38+2x^40

The gray image is a code over GF(2) with n=232, k=15 and d=96.
This code was found by Heurico 1.16 in 3.61 seconds.