The generator matrix

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

generates a code of length 31 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+6x^30+44x^31+7x^32+4x^35+2x^38

The gray image is a code over GF(2) with n=248, k=6 and d=120.
This code was found by Heurico 1.16 in -6.48e-008 seconds.