The generator matrix

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

generates a code of length 15 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+117x^32+72x^33+36x^34+144x^35+963x^36+624x^37+288x^38+1488x^39+3291x^40+3456x^41+840x^42+7920x^43+10476x^44+6288x^45+1152x^46+11376x^47+9600x^48+4920x^49+756x^50+576x^51+1083x^52+63x^56+6x^60

The gray image is a linear code over GF(4) with n=60, k=8 and d=32.
This code was found by Heurico 1.16 in 2.55 seconds.