The generator matrix

 1  0  0  0  1  1  1  X  1 a^2*X  1  1  1 a^2*X
 0  1  0  0  X  1 X+1  1 a^2*X  1 a*X+1 a*X+1 a^2*X  1
 0  0  1  0 a^2*X+1  1 a^2*X a^2*X+1 a*X+1 a^2*X+a  1  X a^2*X  a
 0  0  0  1 a^2  X a*X+a^2 a*X+a^2 a^2*X a^2*X a^2*X+a  a a^2 a^2*X+a^2

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

Homogenous weight enumerator: w(x)=1x^0+396x^32+456x^33+624x^34+984x^35+2310x^36+2088x^37+2160x^38+3000x^39+7890x^40+8280x^41+4560x^42+6408x^43+11808x^44+7608x^45+3408x^46+1896x^47+1641x^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 23.5 seconds.