The generator matrix

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

generates a code of length 74 over F4[X]/(X^2) who´s minimum homogenous weight is 214.

Homogenous weight enumerator: w(x)=1x^0+168x^214+324x^215+471x^216+420x^218+516x^219+432x^220+240x^222+288x^223+177x^224+96x^226+216x^227+126x^228+108x^230+60x^231+75x^232+60x^234+84x^235+60x^236+36x^238+48x^239+60x^240+24x^242+6x^244

The gray image is a linear code over GF(4) with n=296, k=6 and d=214.
This code was found by Heurico 1.16 in 0.125 seconds.