The generator matrix

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

generates a code of length 82 over F4[X]/(X^2) who´s minimum homogenous weight is 220.

Homogenous weight enumerator: w(x)=1x^0+24x^220+267x^224+384x^228+12x^231+438x^232+180x^235+390x^236+1080x^239+363x^240+3240x^243+333x^244+4860x^247+351x^248+2916x^251+306x^252+294x^256+198x^260+237x^264+183x^268+150x^272+69x^276+66x^280+21x^284+9x^288+9x^292+3x^308

The gray image is a linear code over GF(4) with n=328, k=7 and d=220.
This code was found by Heurico 1.16 in 3.84 seconds.