The generator matrix

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

generates a code of length 30 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+50x^26+75x^28+192x^29+396x^30+192x^31+70x^32+34x^34+13x^36+1x^56

The gray image is a code over GF(2) with n=240, k=10 and d=104.
This code was found by Heurico 1.16 in 0.015 seconds.