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  0  1  1  1  1  X  1  1  1  1  1  0  1  1  1 2X+2  X  1 2X  1  1  X  1  1  1  X  2  1  1  1 2X  0  1  X  1  1
 0  X  0 3X+2  2 X+2 2X+2  X  0 X+2 2X X+2 3X  2  2  X  0 X+2  2 3X 2X 3X 2X 3X 3X 2X+2 3X  0  0  X X+2  2  2  X  0 3X+2  X X+2  X  0 2X  0 3X+2 3X+2 2X+2 3X+2 X+2 2X X+2  X  2 X+2 X+2  X 3X+2 3X+2  X  X  X  2 X+2  0  2  0  X 2X+2 2X  2  0  X 2X+2 3X  X 2X
 0  0 2X+2  0  2  0 2X  0  2  2 2X 2X+2 2X+2 2X+2  0  2  0 2X+2 2X 2X+2  2 2X  2  0 2X  0  0  2  2  2  2 2X  0 2X+2  0  2  2 2X 2X  2  0 2X  2  0 2X 2X  2 2X  2  2  2  0 2X 2X 2X+2  0  0  2 2X+2  2 2X+2 2X+2 2X+2  0  0 2X  0 2X+2  2 2X+2 2X+2  2  2  0
 0  0  0 2X+2  0 2X 2X  2  2  2  2  0  0  2 2X+2  2 2X 2X+2 2X+2 2X  0 2X+2 2X+2 2X 2X  0 2X+2  2 2X  0 2X+2 2X+2  0 2X+2 2X  0 2X+2 2X+2 2X 2X+2  2 2X+2  0 2X+2  2 2X+2 2X 2X  2 2X+2 2X+2 2X  2 2X 2X  0 2X+2 2X+2  0 2X+2 2X+2 2X+2 2X 2X+2  2  0  0  0  2  2  0 2X+2 2X  2
 0  0  0  0 2X 2X 2X 2X  0  0  0 2X  0 2X 2X 2X  0  0 2X  0  0 2X  0  0 2X 2X  0 2X 2X 2X 2X  0  0  0 2X  0 2X 2X 2X 2X 2X 2X 2X  0  0  0  0  0 2X  0  0  0 2X 2X 2X 2X 2X  0 2X 2X 2X 2X 2X 2X  0  0 2X  0  0 2X 2X 2X  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+113x^68+136x^69+256x^70+232x^71+506x^72+544x^73+652x^74+548x^75+437x^76+204x^77+188x^78+80x^79+91x^80+40x^81+30x^82+4x^83+17x^84+4x^85+8x^86+2x^88+2x^90+1x^124

The gray image is a code over GF(2) with n=592, k=12 and d=272.
This code was found by Heurico 1.16 in 0.922 seconds.