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

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+432x^32+384x^33+720x^34+864x^35+2280x^36+2304x^37+2736x^38+1248x^39+8619x^40+8064x^41+7728x^42+2592x^43+12600x^44+7680x^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 3.13 seconds.