The generator matrix

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

generates a code of length 15 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+99x^28+225x^32+48x^33+1536x^36+576x^37+768x^39+6324x^40+2592x^41+4608x^43+13554x^44+5184x^45+6912x^47+18174x^48+3888x^49+672x^52+300x^56+75x^60

The gray image is a linear code over GF(4) with n=60, k=8 and d=28.
This code was found by Heurico 1.16 in 2.25 seconds.