The generator matrix

 1  0  1  1  1  1  1  1
 0  1  1  a a+1  0  0  0
 0  0 (a+1)X  0  0  X  0  X
 0  0  0  X  0 (a+1)X (a+1)X (a+1)X
 0  0  0  0 (a+1)X  X aX  0

generates a code of length 8 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+51x^12+219x^16+846x^20+3072x^21+1626x^24+9216x^25+1263x^28+90x^32

The gray image is a linear code over GF(4) with n=32, k=7 and d=12.
This code was found by Heurico 1.16 in 0.0313 seconds.