The generator matrix

 1  0  0  0  1  1  1  1  1  1  1  1  1  1  1
 0  1  0  0  1 (a+1)X  1  a (a+1)X+1 (a+1)X aX aX+1 aX+a+1  a (a+1)X+1
 0  0  1  0 a+1  1  1 X+1  a a+1 (a+1)X+1 (a+1)X X+a+1 (a+1)X+a+1 a+1
 0  0  0  1  1  a X+a aX+a+1  a (a+1)X+a (a+1)X+1 aX  0 a+1 X+a+1
 0  0  0  0 (a+1)X  0  X aX aX  X aX  X (a+1)X  X  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+249x^32+300x^33+564x^34+900x^35+2241x^36+3696x^37+2544x^38+3600x^39+13026x^40+15912x^41+12792x^42+14904x^43+36183x^44+35760x^45+25968x^46+20304x^47+36138x^48+24204x^49+7284x^50+3300x^51+2175x^52+90x^56+9x^60

The gray image is a linear code over GF(4) with n=60, k=9 and d=32.
This code was found by Heurico 1.16 in 27.8 seconds.