The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  X  0  X  1  X  X  1  2  1  1  X  1  X  X
 0  X  0 X^2+X+2 X^2 X^2+X X^2+2  X  2  0 X^2+X X^2+X X^2+2 X+2  X X^2+2 X^2+X+2  X X+2  X X^2+X+2 X^2+X  0  X X^2 X+2 X+2 X^2+X  0  2
 0  0 X^2+2  0 X^2  0  0  2  0 X^2 X^2 X^2  0 X^2  0 X^2+2 X^2+2 X^2+2  2 X^2+2  2 X^2+2 X^2+2 X^2 X^2 X^2+2 X^2+2  2 X^2 X^2+2
 0  0  0 X^2+2  0  0  2 X^2 X^2 X^2 X^2  2 X^2 X^2+2 X^2+2 X^2+2  2 X^2  0  2 X^2 X^2 X^2  2  0 X^2 X^2 X^2+2 X^2 X^2
 0  0  0  0  2  2  2  2  0  0  0  2  2  2  0  2  0  0  0  0  0  0  2  0  0  0  2  2  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+231x^26+240x^27+536x^28+656x^29+868x^30+656x^31+436x^32+240x^33+159x^34+42x^36+22x^38+9x^40

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 30.6 seconds.