The generator matrix

 1  0  1  1  1 X+2  1  1 2X+2  1 3X  1  1  1  1  0  1 X+2  1  1  1 2X+2  1 3X  1  1  1  0  1 X+2  1  1  1 3X  1 2X+2  1  1  1  1  1  0  1  1 X+2  1 2X+2  1 3X  X  X  1  X  X  X  1  1  1  1  0 2X 2X+2  0  1  1  1  X  1  1  1 2X+2 3X  1  1
 0  1 X+1 X+2  3  1 2X+2 3X+3  1 3X  1 2X+1  3 X+1  0  1 X+2  1 3X+3 2X+1 2X+2  1 3X  1  3 3X+3  0  1 X+2  1 X+1 2X+1 2X+2  1 3X  1 X+1  3 2X+1 3X+3  0  1 X+3 X+2  1 2X+2  1 3X  1 3X+2 3X 2X+3 X+2  0 2X  0 2X+2 2X+1 X+3  X  X  1  1 3X+3 3X+3 2X+3  X X+2 X+1  3  X  1 2X  0
 0  0 2X  0  0  0  0  0 2X 2X  0 2X 2X  0  0 2X 2X  0 2X  0 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0 2X 2X  0  0 2X  0 2X  0 2X  0 2X 2X 2X 2X 2X  0 2X  0 2X 2X  0 2X 2X  0 2X 2X 2X  0 2X  0  0  0  0  0 2X  0 2X 2X  0  0  0  0
 0  0  0 2X  0  0  0  0 2X 2X 2X  0  0 2X 2X 2X 2X 2X 2X 2X  0  0  0  0 2X  0 2X  0  0  0  0 2X 2X 2X  0 2X 2X  0 2X 2X 2X 2X  0  0 2X  0  0 2X  0  0 2X  0 2X  0  0  0 2X 2X 2X 2X 2X  0  0 2X 2X 2X 2X  0 2X  0  0  0  0  0
 0  0  0  0 2X  0  0 2X  0  0  0 2X 2X 2X  0  0  0  0 2X 2X  0  0  0  0 2X 2X  0  0  0  0 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0 2X  0  0  0  0  0  0 2X 2X  0 2X 2X 2X 2X 2X  0 2X 2X 2X 2X 2X  0  0 2X 2X 2X  0 2X 2X 2X  0  0
 0  0  0  0  0 2X 2X 2X 2X  0 2X  0 2X  0 2X  0 2X  0 2X 2X 2X 2X  0  0  0  0  0 2X 2X  0  0  0 2X 2X  0  0  0 2X 2X 2X  0 2X 2X 2X  0  0  0 2X 2X  0  0 2X 2X 2X  0 2X 2X 2X  0  0 2X 2X  0  0 2X  0 2X  0 2X  0  0 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+56x^68+172x^69+234x^70+536x^71+235x^72+676x^73+382x^74+612x^75+246x^76+488x^77+166x^78+192x^79+59x^80+4x^81+18x^82+4x^83+8x^84+4x^85+1x^88+1x^92+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 0.484 seconds.