The generator matrix

 1  0  1  1  1  1  1  1
 0  1  1  0 a^2*X+1  X a^2*X+1  a
 0  0 a^2*X  X a*X a^2*X  0  X

generates a code of length 8 over F4[X]/(X^2) who´s minimum homogenous weight is 19.

Homogenous weight enumerator: w(x)=1x^0+72x^19+21x^20+96x^21+144x^23+213x^24+288x^25+168x^27+15x^28+6x^32

The gray image is a linear code over GF(4) with n=32, k=5 and d=19.
This code was found by Heurico 1.16 in 0 seconds.