The generator matrix

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

generates a code of length 30 over Z4[X]/(X^2+2) 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.