The generator matrix

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

generates a code of length 30 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+288x^26+32x^27+700x^28+448x^29+1154x^30+544x^31+634x^32+244x^34+40x^36+10x^38+1x^48

The gray image is a code over GF(2) with n=240, k=12 and d=104.
This code was found by Heurico 1.16 in 34.6 seconds.