The generator matrix

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

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+138x^36+216x^37+384x^38+96x^39+1062x^40+1080x^41+768x^42+576x^43+2904x^44+1800x^45+1152x^46+864x^47+2997x^48+1512x^49+768x^50+54x^52+12x^56

The gray image is a linear code over GF(4) with n=60, k=7 and d=36.
This code was found by Heurico 1.16 in 0.137 seconds.