The generator matrix

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

generates a code of length 14 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+384x^32+432x^33+720x^34+864x^35+2424x^36+2160x^37+2736x^38+1248x^39+8475x^40+8208x^41+7728x^42+2592x^43+12648x^44+7632x^45+4176x^46+1440x^47+1659x^48+9x^56

The gray image is a linear code over GF(4) with n=56, k=8 and d=32.
This code was found by Heurico 1.16 in 2.51 seconds.