The generator matrix

 1  0  0  0  1  1  1  X  1  1  1  0 (a+1)X  1
 0  1  0  0  X  1 X+1  1 (a+1)X aX+1 X+a  1 aX  a
 0  0  1  0 (a+1)X+1  1 (a+1)X (a+1)X+1 aX+1 a+1 (a+1)X+1 (a+1)X+a  1 X+a+1
 0  0  0  1 a+1  X aX+a+1 aX+a+1 (a+1)X  X (a+1)X+a+1 (a+1)X+a+1 X+a+1 (a+1)X+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+408x^32+504x^33+624x^34+984x^35+2214x^36+1944x^37+2160x^38+3000x^39+8106x^40+8424x^41+4560x^42+6408x^43+11616x^44+7560x^45+3408x^46+1896x^47+1701x^48+18x^52

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 2.25 seconds.