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

generates a code of length 74 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+17x^68+4x^69+108x^70+128x^71+255x^72+504x^73+236x^74+384x^75+146x^76+4x^77+156x^78+92x^80+12x^82+1x^140

The gray image is a code over GF(2) with n=592, k=11 and d=272.
This code was found by Heurico 1.16 in 0.5 seconds.