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

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

Homogenous weight enumerator: w(x)=1x^0+56x^68+64x^70+170x^72+640x^73+316x^74+640x^75+55x^76+28x^78+13x^80+20x^82+24x^84+20x^86+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 0.593 seconds.