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

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

Homogenous weight enumerator: w(x)=1x^0+58x^68+78x^70+155x^72+128x^73+304x^74+128x^75+58x^76+32x^78+19x^80+24x^82+20x^84+10x^86+8x^88+1x^136

The gray image is a code over GF(2) with n=296, k=10 and d=136.
This code was found by Heurico 1.16 in 0.358 seconds.