The generator matrix

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

generates a code of length 68 over F4[X]/(X^2) who´s minimum homogenous weight is 192.

Homogenous weight enumerator: w(x)=1x^0+390x^192+204x^193+384x^194+516x^195+1287x^196+636x^197+696x^198+672x^199+1401x^200+732x^201+576x^202+600x^203+1422x^204+480x^205+504x^206+516x^207+1074x^208+432x^209+432x^210+456x^211+918x^212+408x^213+312x^214+204x^215+429x^216+120x^217+144x^218+108x^219+234x^220+60x^221+24x^222+9x^224+3x^228

The gray image is a linear code over GF(4) with n=272, k=7 and d=192.
This code was found by Heurico 1.16 in 1.24 seconds.