The generator matrix

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

generates a code of length 30 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+22x^28+40x^29+17x^30+16x^31+16x^32+8x^33+6x^34+1x^38+1x^40

The gray image is a code over GF(2) with n=120, k=7 and d=56.
This code was found by Heurico 1.16 in 0.00686 seconds.