The generator matrix

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

generates a code of length 95 over F4[X]/(X^2) who´s minimum homogenous weight is 268.

Homogenous weight enumerator: w(x)=1x^0+108x^268+756x^271+354x^272+1356x^275+576x^276+1716x^279+687x^280+2256x^283+600x^284+2208x^287+645x^288+2028x^291+462x^292+1380x^295+351x^296+504x^299+150x^300+84x^303+48x^304+30x^308+15x^312+24x^316+9x^320+15x^324+9x^328+9x^336+3x^340

The gray image is a linear code over GF(4) with n=380, k=7 and d=268.
This code was found by Heurico 1.16 in 2.3 seconds.