The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  X  X  1  X  1  X  1  1  X  2  2  2  2  2  2  2
 0 2X  0  0  0 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0 2X  0 2X  0 2X 2X  0  0  0 2X  0 2X 2X  0
 0  0 2X  0 2X 2X 2X  0  0  0 2X 2X 2X 2X  0  0  0 2X 2X  0 2X 2X  0  0  0 2X 2X 2X 2X  0  0
 0  0  0 2X 2X  0 2X 2X  0 2X 2X  0  0 2X 2X  0 2X  0 2X  0  0 2X 2X  0 2X 2X  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+28x^30+64x^31+31x^32+4x^38

The gray image is a code over GF(2) with n=248, k=7 and d=120.
This code was found by Heurico 1.16 in -6.48e-008 seconds.