The generator matrix
1 0 1 1 1 1 1 1 1 0 1 1 1 1 1
0 1 1 a (a+1)X+a+1 0 (a+1)X+1 a (a+1)X+a+1 1 0 a (a+1)X+a+1 (a+1)X+1 X
0 0 (a+1)X 0 X X (a+1)X X (a+1)X X 0 0 (a+1)X 0 (a+1)X
0 0 0 X aX X aX (a+1)X (a+1)X 0 X (a+1)X aX 0 X
generates a code of length 15 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 36.
Homogenous weight enumerator: w(x)=1x^0+60x^36+36x^37+48x^39+402x^40+180x^41+288x^43+1011x^44+300x^45+432x^47+1029x^48+252x^49+30x^52+24x^56+3x^60
The gray image is a linear code over GF(4) with n=60, k=6 and d=36.
This code was found by Heurico 1.16 in 0.0154 seconds.