The generator matrix

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

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+196x^26+244x^27+432x^28+796x^29+854x^30+784x^31+348x^32+192x^33+176x^34+28x^35+32x^36+4x^37+6x^38+2x^40+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 27.7 seconds.