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

generates a code of length 71 over F4[X]/(X^2) who´s minimum homogenous weight is 188.

Homogenous weight enumerator: w(x)=1x^0+66x^188+243x^192+351x^196+480x^200+561x^204+2136x^208+5529x^212+5547x^216+306x^220+321x^224+234x^228+228x^232+174x^236+108x^240+66x^244+18x^248+9x^252+3x^264+3x^272

The gray image is a linear code over GF(4) with n=284, k=7 and d=188.
This code was found by Heurico 1.16 in 3.22 seconds.