The generator matrix

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

generates a code of length 30 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+34x^27+110x^28+116x^29+81x^30+78x^31+32x^32+6x^33+6x^34+16x^35+24x^36+6x^37+1x^38+1x^40

The gray image is a code over GF(2) with n=120, k=9 and d=54.
This code was found by Heurico 1.13 in 0.016 seconds.