The generator matrix

 1  1  1  1  1  1
 0  X  0  0  0  0
 0  0  X  0  0  0
 0  0  0  X  0  0
 0  0  0  0  X  0
 0  0  0  0  0  X

generates a code of length 6 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+18x^4+135x^8+540x^12+1215x^16+12288x^18+1458x^20+729x^24

The gray image is a linear code over GF(4) with n=24, k=7 and d=4.
This code was found by Heurico 1.16 in 0.0251 seconds.