The generator matrix

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

generates a code of length 95 over F4[X]/(X^2) who´s minimum homogenous weight is 272.

Homogenous weight enumerator: w(x)=1x^0+327x^272+420x^273+360x^274+240x^275+1323x^276+852x^277+552x^278+348x^279+1317x^280+972x^281+768x^282+300x^283+1263x^284+672x^285+432x^286+180x^287+1005x^288+528x^289+312x^290+180x^291+762x^292+540x^293+252x^294+168x^295+639x^296+312x^297+276x^298+72x^299+366x^300+180x^301+60x^302+24x^303+105x^304+120x^305+60x^306+24x^307+51x^308+12x^309+6x^312+3x^316

The gray image is a linear code over GF(4) with n=380, k=7 and d=272.
This code was found by Heurico 1.16 in 1.73 seconds.