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  1  1  1  1  1 2X  1  1  1  0  X 2X+2  X  0  0  X  X
 0  X 2X+2 X+2  0 X+2 2X+2 3X X+2  0 3X 2X+2 3X 2X  2 X+2 3X+2  0 2X+2 3X  0 X+2 2X+2 3X  0 X+2 2X+2 3X 3X+2  0  X 2X+2 2X  2 X+2 3X+2 2X 3X  X  2 3X+2 3X X+2  0 2X  X  0 2X+2 2X+2  2 X+2 X+2 3X+2 3X+2 2X+2  2  2  0 2X 2X 3X 2X 3X  X  X  X X+2  X 3X  X  X  0  0
 0  0 2X  0  0  0 2X  0 2X  0 2X 2X 2X  0 2X  0 2X  0  0  0  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X 2X  0  0 2X 2X  0 2X  0  0 2X 2X 2X 2X  0  0  0 2X 2X  0 2X 2X  0  0  0  0 2X 2X  0  0  0  0 2X 2X  0  0  0  0 2X 2X  0  0
 0  0  0 2X  0  0  0  0  0  0  0  0  0  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0 2X  0 2X  0  0 2X 2X  0  0  0  0 2X 2X 2X 2X  0 2X  0 2X  0  0 2X 2X 2X 2X  0  0 2X  0 2X  0  0  0 2X 2X  0  0  0
 0  0  0  0 2X  0 2X 2X 2X  0  0 2X 2X 2X  0 2X  0 2X 2X 2X  0 2X  0  0  0  0 2X 2X 2X  0  0 2X  0 2X  0  0 2X  0  0  0 2X 2X 2X 2X  0 2X  0  0  0  0 2X 2X  0  0 2X  0 2X 2X 2X 2X  0  0 2X 2X  0  0  0 2X 2X  0  0  0  0
 0  0  0  0  0 2X  0 2X 2X 2X 2X 2X  0 2X 2X  0  0  0 2X 2X 2X  0  0 2X  0  0 2X 2X  0 2X 2X  0  0  0  0 2X  0  0  0  0 2X  0  0 2X 2X  0  0 2X 2X  0 2X 2X 2X 2X 2X 2X  0  0 2X 2X 2X  0  0 2X  0  0 2X 2X  0  0  0  0  0

generates a code of length 73 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+104x^68+256x^70+288x^71+236x^72+480x^73+128x^74+224x^75+104x^76+32x^77+128x^78+66x^80+1x^128

The gray image is a code over GF(2) with n=584, k=11 and d=272.
This code was found by Heurico 1.16 in 0.484 seconds.