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

generates a code of length 75 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+176x^68+12x^69+81x^70+80x^71+200x^72+252x^73+81x^74+352x^75+151x^76+228x^77+54x^78+80x^79+138x^80+20x^81+30x^82+78x^84+9x^86+20x^88+1x^90+3x^92+1x^128

The gray image is a code over GF(2) with n=300, k=11 and d=136.
This code was found by Heurico 1.16 in 6.42 seconds.